Solve x^2-sqrt{3}n=1

$$x ^ { 2 } - \sqrt { 3 } n = 1$$

Solve for n

$$n=\frac{\sqrt{3}\left(x^{2}-1\right)}{3}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-\sqrt{3}n=1-x^{2}$$

The equation is in standard form.

$$\left(-\sqrt{3}\right)n=1-x^{2}$$

Divide both sides by -\sqrt{3}.

$$\frac{\left(-\sqrt{3}\right)n}{-\sqrt{3}}=\frac{1-x^{2}}{-\sqrt{3}}$$

Dividing by -\sqrt{3} undoes the multiplication by -\sqrt{3}.

$$n=\frac{1-x^{2}}{-\sqrt{3}}$$

Divide -x^{2}+1 by -\sqrt{3}.

$$n=-\frac{\sqrt{3}\left(1-x^{2}\right)}{3}$$

Solve for x (complex solution)

$$x=-\sqrt{\sqrt{3}n+1}$$

$$x=\sqrt{\sqrt{3}n+1}$$

Solve for x

$$x=\sqrt{\sqrt{3}n+1}$$

$$x=-\sqrt{\sqrt{3}n+1}\text{, }n\geq -\frac{\sqrt{3}}{3}$$