Name: Anonymous 2010-02-12 22:15
inb4 tex fail
x^4 + ax^3 + bx^2 + cx + d = 0
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}
x^4 + ax^3 + bx^2 + cx + d = 0
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}