Solve 5x^2=3/2

$$5 x ^ { 2 } = \frac { 3 } { 2 }$$

Solve for x

$$x=\frac{\sqrt{30}}{10}\approx 0.547722558$$

$$x=-\frac{\sqrt{30}}{10}\approx -0.547722558$$

Steps by Finding Square Root

Divide both sides by 5.

$$x^{2}=\frac{\frac{3}{2}}{5}$$

Express \frac{\frac{3}{2}}{5} as a single fraction.

$$x^{2}=\frac{3}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$x^{2}=\frac{3}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{10} x=-\frac{\sqrt{30}}{10}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$x^{2}=\frac{\frac{3}{2}}{5}$$

Express \frac{\frac{3}{2}}{5} as a single fraction.

$$x^{2}=\frac{3}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$x^{2}=\frac{3}{10}$$

Subtract \frac{3}{10} from both sides.

$$x^{2}-\frac{3}{10}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{10} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{10}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{10}\right)}}{2}$$

Multiply -4 times -\frac{3}{10}.

$$x=\frac{0±\sqrt{\frac{6}{5}}}{2}$$

Take the square root of \frac{6}{5}.

$$x=\frac{0±\frac{\sqrt{30}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{30}}{10}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{30}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{10} x=-\frac{\sqrt{30}}{10}$$