Solve 5y^2=90

$$5 y ^ { 2 } = 90$$

Solve for y

$$y=3\sqrt{2}\approx 4.242640687$$

$$y=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Divide both sides by 5.

$$y^{2}=\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$y^{2}=18$$

Take the square root of both sides of the equation.

$$y=3\sqrt{2} y=-3\sqrt{2}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$y^{2}=\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$y^{2}=18$$

Subtract 18 from both sides.

$$y^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-18\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-18\right)}}{2}$$

Multiply -4 times -18.

$$y=\frac{0±\sqrt{72}}{2}$$

Take the square root of 72.

$$y=\frac{0±6\sqrt{2}}{2}$$

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

$$y=3\sqrt{2}$$

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

$$y=-3\sqrt{2}$$

The equation is now solved.

$$y=3\sqrt{2} y=-3\sqrt{2}$$