Solve 12x^2=10

$$12 { x }^{ 2 } =10$$

Solve for x

$$x=\frac{\sqrt{30}}{6}\approx 0.912870929$$

$$x=-\frac{\sqrt{30}}{6}\approx -0.912870929$$

Steps by Finding Square Root

Divide both sides by 12.

$$x^{2}=\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{5}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{6} x=-\frac{\sqrt{30}}{6}$$

Steps Using the Quadratic Formula

Divide both sides by 12.

$$x^{2}=\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{5}{6}$$

Subtract \frac{5}{6} from both sides.

$$x^{2}-\frac{5}{6}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{5}{6} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{5}{6}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{5}{6}\right)}}{2}$$

Multiply -4 times -\frac{5}{6}.

$$x=\frac{0±\sqrt{\frac{10}{3}}}{2}$$

Take the square root of \frac{10}{3}.

$$x=\frac{0±\frac{\sqrt{30}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{3}}{2} when ± is plus.

$$x=\frac{\sqrt{30}}{6}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{30}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{6} x=-\frac{\sqrt{30}}{6}$$