Solve 3x^2-2ax-3a=0

$$3 x ^ { 2 } - 2 a x - 3 a = 0$$

Solve for a

$$a=\frac{3x^{2}}{2x+3}$$

$$x\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2ax-3a=-3x^{2}$$

Combine all terms containing a.

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

Divide both sides by -2x-3.

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

Dividing by -2x-3 undoes the multiplication by -2x-3.

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

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

$$a=\frac{3x^{2}}{2x+3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{a\left(a+9\right)}+a}{3}$$

$$x=\frac{-\sqrt{a\left(a+9\right)}+a}{3}$$

Solve for x

$$x=\frac{\sqrt{a\left(a+9\right)}+a}{3}$$

$$x=\frac{-\sqrt{a\left(a+9\right)}+a}{3}\text{, }a\leq -9\text{ or }a\geq 0$$