4y(2y+30)=180

Solution for 4y(2y+30)=180 equation:

4y(2y+30)=180

We move all terms to the left:

4y(2y+30)-(180)=0

We multiply parentheses

8y^2+120y-180=0

a = 8; b = 120; c = -180;
Δ = b2-4ac
Δ = 1202-4·8·(-180)
Δ = 20160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{35}}{2*8}=\frac{-120-24\sqrt{35}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{35}}{2*8}=\frac{-120+24\sqrt{35}}{16}
$