Solve -a=sqrt{2a^2-3ab}

$$- a = \sqrt { 2 a ^ { 2 } - 3 a b }$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a}{3}\text{, }&a\leq 0\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{2a^{2}-3ab}=-a$$

Square both sides of the equation.

$$\left(-3a\right)b+2a^{2}=a^{2}$$

Subtract 2a^{2} from both sides of the equation.

$$\left(-3a\right)b+2a^{2}-2a^{2}=a^{2}-2a^{2}$$

Subtracting 2a^{2} from itself leaves 0.

$$\left(-3a\right)b=a^{2}-2a^{2}$$

Subtract 2a^{2} from a^{2}.

$$\left(-3a\right)b=-a^{2}$$

Divide both sides by -3a.

$$\frac{\left(-3a\right)b}{-3a}=-\frac{a^{2}}{-3a}$$

Dividing by -3a undoes the multiplication by -3a.

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

Divide -a^{2} by -3a.

$$b=\frac{a}{3}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a=3b\text{, }&arg(b)\geq \pi \text{ or }b=0\end{matrix}\right.$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{a}{3}\text{, }&arg(a)\geq \pi \text{ or }a=0\\b\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a=3b\text{, }&b\leq 0\end{matrix}\right.$$