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The muthafukken quartic formula

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}

Name: Anonymous 2010-02-13 23:55

i can't prove this wrong

Name: Anonymous 2010-02-15 2:29

retest

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}

Name: Anonymous 2010-02-15 5:44

awesome.

Name: Anonymous 2010-02-18 19:30

Thx to spoil my favorite page

Name: Anonymous 2010-02-18 22:57

Now, post the quintic formula, and we'll be proud of you.

Name: Anonymous 2010-02-18 23:34

>>6
not abel to do it

Name: Anonymous 2010-02-19 0:59

>>7
I get it!

Name: mo‮8pE! to‬pui‮ !1uHaijp7IU!n9e4aOufPFUPnvI 2010-03-01 16:37

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Name: Anonymous 2010-03-01 17:34

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Name: Anonymous 2010-03-01 17:34

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Name: Anonymous 2010-03-01 17:34

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Name: Anonymous 2010-03-01 17:34

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Name: Anonymous 2010-03-01 17:35

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Name: Anonymous 2010-03-01 17:35

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