Solve y^2=2zx

$${ y }^{ 2 } =2zx$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{2}}{2z}\text{, }&z\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2zx=y^{2}$$

Divide both sides by 2z.

$$\frac{2zx}{2z}=\frac{y^{2}}{2z}$$

Dividing by 2z undoes the multiplication by 2z.

$$x=\frac{y^{2}}{2z}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y^{2}}{2z}\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2zx=y^{2}$$

Divide both sides by 2z.

$$\frac{2zx}{2z}=\frac{y^{2}}{2z}$$

Dividing by 2z undoes the multiplication by 2z.

$$x=\frac{y^{2}}{2z}$$

Solve for y (complex solution)

$$y=-\sqrt{x}\sqrt{2z}$$

$$y=\sqrt{x}\sqrt{2z}$$

Solve for y

$$y=\sqrt{2xz}$$

$$y=-\sqrt{2xz}\text{, }\left(x\geq 0\text{ and }z\geq 0\right)\text{ or }\left(z\leq 0\text{ and }x\leq 0\right)$$