Solve x^2-2ax=6ab+9b^2

$$x ^ { 2 } - 2 a x = 6 a b + 9 b ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{x-3b}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6ab from both sides.

$$x^{2}-2ax-6ab=9b^{2}$$

Subtract x^{2} from both sides.

$$-2ax-6ab=9b^{2}-x^{2}$$

Combine all terms containing a.

$$\left(-2x-6b\right)a=9b^{2}-x^{2}$$

Divide both sides by -2x-6b.

$$\frac{\left(-2x-6b\right)a}{-2x-6b}=\frac{9b^{2}-x^{2}}{-2x-6b}$$

Dividing by -2x-6b undoes the multiplication by -2x-6b.

$$a=\frac{9b^{2}-x^{2}}{-2x-6b}$$

Divide 9b^{2}-x^{2} by -2x-6b.

$$a=\frac{x-3b}{2}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{x-3b}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6ab from both sides.

$$x^{2}-2ax-6ab=9b^{2}$$

Subtract x^{2} from both sides.

$$-2ax-6ab=9b^{2}-x^{2}$$

Combine all terms containing a.

$$\left(-2x-6b\right)a=9b^{2}-x^{2}$$

Divide both sides by -2x-6b.

$$\frac{\left(-2x-6b\right)a}{-2x-6b}=\frac{9b^{2}-x^{2}}{-2x-6b}$$

Dividing by -2x-6b undoes the multiplication by -2x-6b.

$$a=\frac{9b^{2}-x^{2}}{-2x-6b}$$

Divide 9b^{2}-x^{2} by -2x-6b.

$$a=\frac{x-3b}{2}$$

Solve for b

$$b=-\frac{x}{3}$$

$$b=\frac{x-2a}{3}$$