Solve x^2+xy-2z^2=0

$$x ^ { 2 } + x y - 2 z ^ { 2 } = 0$$

Solve for y

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$xy-2z^{2}=-x^{2}$$

Add 2z^{2} to both sides.

$$xy=-x^{2}+2z^{2}$$

The equation is in standard form.

$$xy=2z^{2}-x^{2}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{2z^{2}-x^{2}}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide -x^{2}+2z^{2} by x.

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

Solve for x

$$x=\frac{\sqrt{y^{2}+8z^{2}}-y}{2}$$

$$x=\frac{-\sqrt{y^{2}+8z^{2}}-y}{2}$$