Solve x^2-5ax-1=0

$$x ^ { 2 } - 5 a x - 1 = 0$$

Solve for a

$$a=\frac{x}{5}-\frac{1}{5x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$-5ax-1=-x^{2}$$

Add 1 to both sides.

$$-5ax=-x^{2}+1$$

The equation is in standard form.

$$\left(-5x\right)a=1-x^{2}$$

Divide both sides by -5x.

$$\frac{\left(-5x\right)a}{-5x}=\frac{1-x^{2}}{-5x}$$

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

$$a=\frac{1-x^{2}}{-5x}$$

Divide -x^{2}+1 by -5x.

$$a=\frac{x}{5}-\frac{1}{5x}$$

Solve for x

$$x=\frac{\sqrt{25a^{2}+4}+5a}{2}$$

$$x=\frac{-\sqrt{25a^{2}+4}+5a}{2}$$