Solve 80y^2=9

$$80 y ^ { 2 } = 9$$

Solve for y

$$y=\frac{3\sqrt{5}}{20}\approx 0.335410197$$

$$y=-\frac{3\sqrt{5}}{20}\approx -0.335410197$$

Steps by Finding Square Root

Divide both sides by 80.

$$y^{2}=\frac{9}{80}$$

Take the square root of both sides of the equation.

$$y=\frac{3\sqrt{5}}{20} y=-\frac{3\sqrt{5}}{20}$$

Steps Using the Quadratic Formula

Divide both sides by 80.

$$y^{2}=\frac{9}{80}$$

Subtract \frac{9}{80} from both sides.

$$y^{2}-\frac{9}{80}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{80} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{80}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{9}{80}\right)}}{2}$$

Multiply -4 times -\frac{9}{80}.

$$y=\frac{0±\sqrt{\frac{9}{20}}}{2}$$

Take the square root of \frac{9}{20}.

$$y=\frac{0±\frac{3\sqrt{5}}{10}}{2}$$

Now solve the equation y=\frac{0±\frac{3\sqrt{5}}{10}}{2} when ± is plus.

$$y=\frac{3\sqrt{5}}{20}$$

Now solve the equation y=\frac{0±\frac{3\sqrt{5}}{10}}{2} when ± is minus.

$$y=-\frac{3\sqrt{5}}{20}$$

The equation is now solved.

$$y=\frac{3\sqrt{5}}{20} y=-\frac{3\sqrt{5}}{20}$$