Solve 5y^2+15=75

$$5 y ^ { 2 } + 15 = 75$$

Solve for y

$$y=2\sqrt{3}\approx 3.464101615$$

$$y=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

Subtract 15 from both sides.

$$5y^{2}=75-15$$

Subtract 15 from 75 to get 60.

$$5y^{2}=60$$

Divide both sides by 5.

$$y^{2}=\frac{60}{5}$$

Divide 60 by 5 to get 12.

$$y^{2}=12$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 75 from both sides.

$$5y^{2}+15-75=0$$

Subtract 75 from 15 to get -60.

$$5y^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 5\left(-60\right)}}{2\times 5}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 5\left(-60\right)}}{2\times 5}$$

Multiply -4 times 5.

$$y=\frac{0±\sqrt{-20\left(-60\right)}}{2\times 5}$$

Multiply -20 times -60.

$$y=\frac{0±\sqrt{1200}}{2\times 5}$$

Take the square root of 1200.

$$y=\frac{0±20\sqrt{3}}{2\times 5}$$

Multiply 2 times 5.

$$y=\frac{0±20\sqrt{3}}{10}$$

Now solve the equation y=\frac{0±20\sqrt{3}}{10} when ± is plus.

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

Now solve the equation y=\frac{0±20\sqrt{3}}{10} when ± is minus.

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

The equation is now solved.

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