Solve {l}{y_{1}=3(x^3-x)}{y_{2}=0}

$$\left. \begin{array} { l } { y _ { 1 } = 3 ( x ^ { 3 } - x ) } \\ { y _ { 2 } = 0 } \end{array} \right.$$

Solve for x

$$x=-\frac{\sqrt[3]{3}\left(1+\sqrt{3}i\right)\left(\sqrt{3y_{1}^{2}-4}+\sqrt{3}y_{1}\right)^{-\frac{1}{3}}\left(-\left(6^{\frac{2}{3}}i+2^{\frac{2}{3}}\sqrt[6]{3}\right)\left(\sqrt{3y_{1}^{2}-4}+\sqrt{3}y_{1}\right)^{\frac{2}{3}}+4\sqrt[3]{2}\sqrt[6]{3}\right)}{24}$$

$$x=\frac{2^{\frac{2}{3}}\left(\frac{\sqrt{3y_{1}^{2}-4}}{3^{\frac{5}{2}}}+\frac{y_{1}}{9}\right)^{-\frac{1}{3}}\left(\left(3\left(\sqrt{3y_{1}^{2}-4}+\sqrt{3}y_{1}\right)\right)^{\frac{2}{3}}+6^{\frac{2}{3}}\right)}{18}$$

$$x=-\frac{\sqrt[3]{3}\left(-\sqrt{3}i+1\right)\left(\sqrt{3y_{1}^{2}-4}+\sqrt{3}y_{1}\right)^{-\frac{1}{3}}\left(\left(6^{\frac{2}{3}}i-2^{\frac{2}{3}}\sqrt[6]{3}\right)\left(\sqrt{3y_{1}^{2}-4}+\sqrt{3}y_{1}\right)^{\frac{2}{3}}+4\sqrt[3]{2}\sqrt[6]{3}\right)}{24}\text{, }y_{2}=0$$