Solve 144y^2-5=30

$$144 y ^ { 2 } - 5 = 30$$

Solve for y

$$y=\frac{\sqrt{35}}{12}\approx 0.493006649$$

$$y=-\frac{\sqrt{35}}{12}\approx -0.493006649$$

Steps by Finding Square Root

Add 5 to both sides.

$$144y^{2}=30+5$$

Add 30 and 5 to get 35.

$$144y^{2}=35$$

Divide both sides by 144.

$$y^{2}=\frac{35}{144}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{35}}{12} y=-\frac{\sqrt{35}}{12}$$

Steps Using the Quadratic Formula

Subtract 30 from both sides.

$$144y^{2}-5-30=0$$

Subtract 30 from -5 to get -35.

$$144y^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 144 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 144\left(-35\right)}}{2\times 144}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 144\left(-35\right)}}{2\times 144}$$

Multiply -4 times 144.

$$y=\frac{0±\sqrt{-576\left(-35\right)}}{2\times 144}$$

Multiply -576 times -35.

$$y=\frac{0±\sqrt{20160}}{2\times 144}$$

Take the square root of 20160.

$$y=\frac{0±24\sqrt{35}}{2\times 144}$$

Multiply 2 times 144.

$$y=\frac{0±24\sqrt{35}}{288}$$

Now solve the equation y=\frac{0±24\sqrt{35}}{288} when ± is plus.

$$y=\frac{\sqrt{35}}{12}$$

Now solve the equation y=\frac{0±24\sqrt{35}}{288} when ± is minus.

$$y=-\frac{\sqrt{35}}{12}$$

The equation is now solved.

$$y=\frac{\sqrt{35}}{12} y=-\frac{\sqrt{35}}{12}$$