Solve (2)y=x^2+ax-a

$$( 2 ) y = x ^ { 2 } + a x - a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}-2y}{x-1}\text{, }&x\neq 1\\a\in \mathrm{C}\text{, }&y=\frac{1}{2}\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax-a=2y$$

Subtract x^{2} from both sides.

$$ax-a=2y-x^{2}$$

Combine all terms containing a.

$$\left(x-1\right)a=2y-x^{2}$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)a}{x-1}=\frac{2y-x^{2}}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$a=\frac{2y-x^{2}}{x-1}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x^{2}-2y}{x-1}\text{, }&x\neq 1\\a\in \mathrm{R}\text{, }&y=\frac{1}{2}\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax-a=2y$$

Subtract x^{2} from both sides.

$$ax-a=2y-x^{2}$$

Combine all terms containing a.

$$\left(x-1\right)a=2y-x^{2}$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)a}{x-1}=\frac{2y-x^{2}}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$a=\frac{2y-x^{2}}{x-1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8y+a^{2}+4a}-a}{2}$$

$$x=\frac{-\sqrt{8y+a^{2}+4a}-a}{2}$$

Solve for x

$$x=\frac{\sqrt{8y+a^{2}+4a}-a}{2}$$

$$x=\frac{-\sqrt{8y+a^{2}+4a}-a}{2}\text{, }y\geq -\frac{a^{2}}{8}-\frac{a}{2}$$