Question

$$\frac { x } { y } = \frac { 5 } { 2 } \frac { 3 x ^ { 2 } + 5 y ^ { 2 } } { 5 x ^ { 2 } - 5 y ^ { 2 } }$$

Solve for x

$x=\frac{9^{\frac{2}{3}}\left(\sqrt[3]{2\sqrt{3165}\left(|y|\right)^{3}+117y^{3}}+\sqrt[3]{-2\sqrt{3165}\left(|y|\right)^{3}+117y^{3}}+\sqrt[3]{9}y\right)}{18}$
$y\neq 0$

Solve for y

$y=\frac{\sqrt[3]{15\sqrt{3165}\left(|x|\right)^{3}+802x^{3}}+\sqrt[3]{-15\sqrt{3165}\left(|x|\right)^{3}+802x^{3}}-2x}{15}$
$x\neq 0$