2(y+25)(2y-30)=180

Solution for 2(y+25)(2y-30)=180 equation:

2(y+25)(2y-30)=180

We move all terms to the left:

2(y+25)(2y-30)-(180)=0

We multiply parentheses ..

2(+2y^2-30y+50y-750)-180=0

We multiply parentheses

4y^2-60y+100y-1500-180=0

We add all the numbers together, and all the variables

4y^2+40y-1680=0

a = 4; b = 40; c = -1680;
Δ = b2-4ac
Δ = 402-4·4·(-1680)
Δ = 28480
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:

$\sqrt{\Delta}=\sqrt{28480}=\sqrt{64*445}=\sqrt{64}*\sqrt{445}=8\sqrt{445}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{445}}{2*4}=\frac{-40-8\sqrt{445}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{445}}{2*4}=\frac{-40+8\sqrt{445}}{8}
$