Solve 5x^2=9

$$5 x ^ { 2 } = 9$$

Solve for x

$$x = \frac{3 \sqrt{5}}{5} \approx 1.341640786$$

$$x = -\frac{3 \sqrt{5}}{5} \approx -1.341640786$$

Steps by Finding Square Root

Divide both sides by 5.

$$x^{2}=\frac{9}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{5}}{5} x=-\frac{3\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$x^{2}=\frac{9}{5}$$

Subtract \frac{9}{5} from both sides.

$$x^{2}-\frac{9}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{5}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{5}\right)}}{2}$$

Multiply -4 times -\frac{9}{5}.

$$x=\frac{0±\sqrt{\frac{36}{5}}}{2}$$

Take the square root of \frac{36}{5}.

$$x=\frac{0±\frac{6\sqrt{5}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{5}}{5}}{2} when ± is plus.

$$x=\frac{3\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{5}}{5}}{2} when ± is minus.

$$x=-\frac{3\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}}{5} x=-\frac{3\sqrt{5}}{5}$$