Solve 13x^2=6

$$13 x ^ { 2 } = 6$$

Solve for x

$$x=\frac{\sqrt{78}}{13}\approx 0.67936622$$

$$x=-\frac{\sqrt{78}}{13}\approx -0.67936622$$

Steps by Finding Square Root

Divide both sides by 13.

$$x^{2}=\frac{6}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{78}}{13} x=-\frac{\sqrt{78}}{13}$$

Steps Using the Quadratic Formula

Divide both sides by 13.

$$x^{2}=\frac{6}{13}$$

Subtract \frac{6}{13} from both sides.

$$x^{2}-\frac{6}{13}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{6}{13} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{6}{13}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{6}{13}\right)}}{2}$$

Multiply -4 times -\frac{6}{13}.

$$x=\frac{0±\sqrt{\frac{24}{13}}}{2}$$

Take the square root of \frac{24}{13}.

$$x=\frac{0±\frac{2\sqrt{78}}{13}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{78}}{13}}{2} when ± is plus.

$$x=\frac{\sqrt{78}}{13}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{78}}{13}}{2} when ± is minus.

$$x=-\frac{\sqrt{78}}{13}$$

The equation is now solved.

$$x=\frac{\sqrt{78}}{13} x=-\frac{\sqrt{78}}{13}$$