Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{5y^{4}+uy^{2}-9y^{2}-5u}+4y}{y^{2}-5}\text{; }x=\frac{-\sqrt{5y^{4}+uy^{2}-9y^{2}-5u}+4y}{y^{2}-5}\text{, }&y\neq -\sqrt{5}\text{ and }y\neq \sqrt{5}\\x=\frac{-5y^{2}-u}{8y}\text{, }&y=-\sqrt{5}\text{ or }y=\sqrt{5}\end{matrix}\right.
Solve for u
u=\left(xy\right)^{2}-5y^{2}-8xy-5x^{2}
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{5y^{4}+uy^{2}-9y^{2}-5u}+4y}{y^{2}-5}\text{; }x=\frac{-\sqrt{5y^{4}+uy^{2}-9y^{2}-5u}+4y}{y^{2}-5}\text{, }&\left(y\neq -\sqrt{5}\text{ and }u=-\frac{y^{2}\left(5y^{2}-9\right)}{y^{2}-5}\text{ and }|y|<\sqrt{5}\right)\text{ or }\left(u\leq -\frac{y^{2}\left(5y^{2}-9\right)}{y^{2}-5}\text{ and }y>-\sqrt{5}\text{ and }|y|<\sqrt{5}\right)\text{ or }\left(u\geq -\frac{y^{2}\left(5y^{2}-9\right)}{y^{2}-5}\text{ and }|y|>\sqrt{5}\right)\text{ or }\left(u=-\frac{y^{2}\left(5y^{2}-9\right)}{y^{2}-5}\text{ and }|y|\neq \sqrt{5}\right)\\x=\frac{-5y^{2}-u}{8y}\text{, }&|y|=\sqrt{5}\end{matrix}\right.
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