Επίλυση 6-2x^3+15x=0

$$6-2 { x }^{ 3 } +15x=0$$

Λύση ως προς x (complex solution)

$$x=-\frac{4^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(6+\sqrt{214}i\right)^{-\frac{1}{3}}\left(\left(6+\sqrt{214}i\right)^{\frac{2}{3}}\left(-\sqrt{3}i-1\right)+5\times 4^{\frac{2}{3}}\right)}{16}\approx -2,511029886+2,220446049 \cdot 10^{-16}i$$

$$x=\frac{2^{\frac{2}{3}}\left(6+\sqrt{214}i\right)^{-\frac{1}{3}}\left(\left(2\left(6+\sqrt{214}i\right)\right)^{\frac{2}{3}}+10\right)}{4}\approx 2,920161057$$

$$x=-\frac{4^{\frac{2}{3}}\left(6+\sqrt{214}i\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(\left(-1+\sqrt{3}i\right)\left(6+\sqrt{214}i\right)^{\frac{2}{3}}+5\times 4^{\frac{2}{3}}\right)}{16}\approx -0,40913117+2,844946501 \cdot 10^{-16}i$$

Λύση ως προς x

$$x=-\frac{\sqrt{10}\left(\sqrt{3}\sin(\frac{\arccos(\frac{3\sqrt{10}}{25})}{3})+\cos(\frac{\arccos(\frac{3\sqrt{10}}{25})}{3})\right)}{2}\approx -2,511029886$$

$$x=\sqrt{10}\cos(\frac{\arccos(\frac{3\sqrt{10}}{25})}{3})\approx 2,920161057$$

$$x=\frac{\sqrt{10}\left(\sqrt{3}\sin(\frac{\arccos(\frac{3\sqrt{10}}{25})}{3})-\cos(\frac{\arccos(\frac{3\sqrt{10}}{25})}{3})\right)}{2}\approx -0,40913117$$