Solve yx2-y=x^2

$$yx2-y = { x }^{ 2 }$$

Solve for x_2 (complex solution)

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

Steps for Solving Linear Equation

Add y to both sides.

$$yx_{2}=x^{2}+y$$

Divide both sides by y.

$$\frac{yx_{2}}{y}=\frac{x^{2}+y}{y}$$

Dividing by y undoes the multiplication by y.

$$x_{2}=\frac{x^{2}+y}{y}$$

Solve for x_2

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

Steps for Solving Linear Equation

Add y to both sides.

$$yx_{2}=x^{2}+y$$

Divide both sides by y.

$$\frac{yx_{2}}{y}=\frac{x^{2}+y}{y}$$

Dividing by y undoes the multiplication by y.

$$x_{2}=\frac{x^{2}+y}{y}$$

Solve for x (complex solution)

$$x=-\sqrt{y}\sqrt{x_{2}-1}$$

$$x=\sqrt{y}\sqrt{x_{2}-1}$$

Solve for x

$$x=\sqrt{y\left(x_{2}-1\right)}$$

$$x=-\sqrt{y\left(x_{2}-1\right)}\text{, }\left(y\geq 0\text{ and }x_{2}\geq 1\right)\text{ or }\left(x_{2}\leq 1\text{ and }y\leq 0\right)$$