Solve y=ax^2-10ax+2a

$$y = a x ^ { 2 } - 10 a x + 2 a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{x^{2}-10x+2}\text{, }&x\neq \sqrt{23}+5\text{ and }x\neq 5-\sqrt{23}\\a\in \mathrm{C}\text{, }&\left(x=5-\sqrt{23}\text{ or }x=\sqrt{23}+5\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}-10ax+2a=y$$

Combine all terms containing a.

$$\left(x^{2}-10x+2\right)a=y$$

Divide both sides by x^{2}-10x+2.

$$\frac{\left(x^{2}-10x+2\right)a}{x^{2}-10x+2}=\frac{y}{x^{2}-10x+2}$$

Dividing by x^{2}-10x+2 undoes the multiplication by x^{2}-10x+2.

$$a=\frac{y}{x^{2}-10x+2}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{x^{2}-10x+2}\text{, }&x\neq \sqrt{23}+5\text{ and }x\neq 5-\sqrt{23}\\a\in \mathrm{R}\text{, }&\left(x=5-\sqrt{23}\text{ or }x=\sqrt{23}+5\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}-10ax+2a=y$$

Combine all terms containing a.

$$\left(x^{2}-10x+2\right)a=y$$

Divide both sides by x^{2}-10x+2.

$$\frac{\left(x^{2}-10x+2\right)a}{x^{2}-10x+2}=\frac{y}{x^{2}-10x+2}$$

Dividing by x^{2}-10x+2 undoes the multiplication by x^{2}-10x+2.

$$a=\frac{y}{x^{2}-10x+2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{a\left(y+23a\right)}+5a}{a}\text{; }x=\frac{-\sqrt{a\left(y+23a\right)}+5a}{a}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{a\left(y+23a\right)}+5a}{a}\text{; }x=\frac{-\sqrt{a\left(y+23a\right)}+5a}{a}\text{, }&\left(y\leq -23a\text{ and }a<0\right)\text{ or }\left(y\geq -23a\text{ and }a>0\right)\text{ or }\left(a\neq 0\text{ and }y=-23a\right)\\x\in \mathrm{R}\text{, }&a=0\text{ and }y=0\end{matrix}\right.$$