The quadratic, cubic, and quartic formulas.

Just for fun, since I have no life.

Quadratic:  0=x^2+ax+b

x=\frac{-b+\sqrt{b^2-4ac}}{2}

Cubic: 0=x^3+ax^2+bx+c

\sqrt[3]{-\frac{q}{2} + \sqrt{\frac{\left(c+\frac{2a^3-9ab}{27}\right)^2}{4}+\frac{\left(b-\frac{a^2}{3}\right)^3}{27}}} - \frac{\left(b-\frac{a^2}{3}\right)}{3\sqrt[3]{-\frac{q}{2} + \sqrt{\frac{\left(c+\frac{2a^3-9ab}{27}\right)^2}{4}+\frac{\left(b-\frac{a^2}{3}\right)^3}{27}}}} - \frac{a}{3}

Quartic: 0=x^4+ax^3+bx^2+cx+d

x=-\frac{a}{4} + \frac{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)} + \sqrt{-(3\left(-\frac{3a^2}{8}+b\right) + 2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right) + \frac{2\frac{a^3}{8}-\frac{ab}{2}+c\right)}{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)}})}}{2}

inb4 the board shits itself on that last one.

Oh fuck me, how am I going to find that??  >_>

Hang on...

Maybe this will work. (THANK YOU UNDO FUNCTION!)

x=-\frac{a}{4} + \frac{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)} + \sqrt{-(3\left(-\frac{3a^2}{8}+b\right) + 2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right) + \frac{2\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)}{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)}})}}{2}

*cross fingers*

A bit nicer (maybe):

x=-\frac{a}{4} + \left(\frac{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)} + \sqrt{-(3\left(-\frac{3a^2}{8}+b\right) + 2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right) + \frac{2\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)}{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)}})}}{2}\right)

>>2
haha, there's that giant horizontal bar... then a screen later, there's this tiny little "2" below it.

Good effort overall, but you're forgetting that there's more than 1 root.  Even for the quadratic equation, you neglected the negative (possibility on the) sqrt.

Did you use mathematica?  Last I recall, brute forcing the quartic equation by hand should take hrs, if not days.

Too bad we can't have quintic equations... Bring radicals!

Goddamn, good sir, you've broke the board!

>>4
>Did you use mathematica?

I did it in texnic center using the formula on wikipedia.  They give it in several steps, calculating a bunch of intermediate variables along the way to make the formulas smaller.  I wanted to see what it looked like totally expanded out.

http://en.wikipedia.org/wiki/Quartic_equation#The_general_case.2C_along_Ferrari.27s_lines

And I left the \pm's out on purpose. :p

Slightly retouched, and fixed one pair of parenthesis that was bugging me.  (Now if only I could delete those other two.  Worthless textboards. :/ )

x=-\frac{a}{4} + \frac{1}{2}\left(\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)} + \sqrt{-\left(3\left(-\frac{3a^2}{8}+b\right) + 2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right) + \frac{2\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)}{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)}}\right)}\right)

facepalm.

x=-\frac{a}{4} + \frac{1}{2}\left(\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)} + \sqrt{-\left(3\left(-\frac{3a^2}{8}+b\right) + 2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right) + \frac{2\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)}{\sqrt{\left(-\frac{3a^2}{8}+b\right)+2\left(-\frac{5}{6}\left(-\frac{3a^2}{8}+b\right) + \sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)} - \frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)}{3\sqrt[3]{\left(-\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)}{2}+\sqrt{\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^3}{108}+\frac{\left(-\frac{3a^2}{8}+b\right) \left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)}{3}-\frac{\left(\frac{a^3}{8}-\frac{ab}{2}+c\right)^2}{8}\right)^2}{4}+\frac{\left(-\frac{\left(-\frac{3a^2}{8}+b\right)^2}{12}-\left(-\frac{3a^4}{256} + \frac{ba^2}{16}-\frac{ac}{4}+d\right)\right)^3}{27}}\right)}}\right)}}\right)}\right)

>>7
=1