$$x^{2}-3=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-3$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)}}{2}$$
Square $0$.$$x=\frac{0±\sqrt{-4\left(-3\right)}}{2}$$
Multiply $-4$ times $-3$.$$x=\frac{0±\sqrt{12}}{2}$$
Take the square root of $12$.$$x=\frac{0±2\sqrt{3}}{2}$$
Now solve the equation $x=\frac{0±2\sqrt{3}}{2}$ when $±$ is plus.$$x=\sqrt{3}$$
Now solve the equation $x=\frac{0±2\sqrt{3}}{2}$ when $±$ is minus.$$x=-\sqrt{3}$$
The equation is now solved.$$x=\sqrt{3}$$ $$x=-\sqrt{3}$$