Solve x^2+4ax-5a=0

$$x ^ { 2 } + 4 a x - 5 a = 0$$

Solve for a

$$a=-\frac{x^{2}}{4x-5}$$

$$x\neq \frac{5}{4}$$

Steps for Solving Linear Equation

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

$$4ax-5a=-x^{2}$$

Combine all terms containing a.

$$\left(4x-5\right)a=-x^{2}$$

Divide both sides by 4x-5.

$$\frac{\left(4x-5\right)a}{4x-5}=-\frac{x^{2}}{4x-5}$$

Dividing by 4x-5 undoes the multiplication by 4x-5.

$$a=-\frac{x^{2}}{4x-5}$$

Solve for x (complex solution)

$$x=\sqrt{a\left(4a+5\right)}-2a$$

$$x=-\sqrt{a\left(4a+5\right)}-2a$$

Solve for x

$$x=\sqrt{a\left(4a+5\right)}-2a$$

$$x=-\sqrt{a\left(4a+5\right)}-2a\text{, }a\leq -\frac{5}{4}\text{ or }a\geq 0$$