Solve 3y^2=80

$$3 y ^ { 2 } = 80$$

Solve for y

$$y = \frac{4 \sqrt{15}}{3} \approx 5.163977795$$

$$y = -\frac{4 \sqrt{15}}{3} \approx -5.163977795$$

Steps by Finding Square Root

Divide both sides by 3.

$$y^{2}=\frac{80}{3}$$

Take the square root of both sides of the equation.

$$y=\frac{4\sqrt{15}}{3} y=-\frac{4\sqrt{15}}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$y^{2}=\frac{80}{3}$$

Subtract \frac{80}{3} from both sides.

$$y^{2}-\frac{80}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{80}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{80}{3}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{80}{3}\right)}}{2}$$

Multiply -4 times -\frac{80}{3}.

$$y=\frac{0±\sqrt{\frac{320}{3}}}{2}$$

Take the square root of \frac{320}{3}.

$$y=\frac{0±\frac{8\sqrt{15}}{3}}{2}$$

Now solve the equation y=\frac{0±\frac{8\sqrt{15}}{3}}{2} when ± is plus.

$$y=\frac{4\sqrt{15}}{3}$$

Now solve the equation y=\frac{0±\frac{8\sqrt{15}}{3}}{2} when ± is minus.

$$y=-\frac{4\sqrt{15}}{3}$$

The equation is now solved.

$$y=\frac{4\sqrt{15}}{3} y=-\frac{4\sqrt{15}}{3}$$