$\left\{\begin{matrix}x=\frac{\sqrt{25z^{2}-20yz}}{2}+\frac{5z}{2}-y\text{, }&\left(z\neq 0\text{ and }arg(z)<\pi \right)\text{ or }y\neq 0\\x=-\frac{\sqrt{25z^{2}-20yz}}{2}+\frac{5z}{2}-y\text{, }&\left(arg(z)\geq \pi \text{ and }z\neq 0\right)\text{ or }y\neq 0\end{matrix}\right.$

$y=\sqrt{x}\sqrt{5z}-x$
$y=-\sqrt{x}\sqrt{5z}-x\text{, }x\neq 0$

$\left\{\begin{matrix}x=\frac{\sqrt{25z^{2}-20yz}}{2}+\frac{5z}{2}-y\text{, }&\left(y\neq 0\text{ and }z=\frac{4y}{5}\right)\text{ or }\left(y\neq 0\text{ and }z\leq \frac{4y}{5}\text{ and }z\leq 0\right)\text{ or }\left(y\neq 0\text{ and }z\geq 0\text{ and }z\geq \frac{4y}{5}\right)\text{ or }\left(z>0\text{ and }z\geq \frac{4y}{5}\right)\\x=-\frac{\sqrt{25z^{2}-20yz}}{2}+\frac{5z}{2}-y\text{, }&\left(y\neq 0\text{ and }z=\frac{4y}{5}\right)\text{ or }\left(y\neq 0\text{ and }z\leq \frac{4y}{5}\text{ and }z\leq 0\right)\text{ or }\left(y\neq 0\text{ and }z\geq 0\text{ and }z\geq \frac{4y}{5}\right)\text{ or }\left(z<0\text{ and }z\leq \frac{4y}{5}\right)\end{matrix}\right.$

$\left\{\begin{matrix}y=\sqrt{5xz}-x\text{, }&\left(z\geq 0\text{ and }x>0\right)\text{ or }\left(z\leq 0\text{ and }x<0\right)\\y=-\sqrt{5xz}-x\text{, }&z\leq 0\text{ and }x<0\\y=-\sqrt{5xz}-x\text{, }&z\geq 0\text{ and }x>0\end{matrix}\right.$