2y(y+15)+63=180

Solution for 2y(y+15)+63=180 equation:

2y(y+15)+63=180

We move all terms to the left:

2y(y+15)+63-(180)=0

We add all the numbers together, and all the variables

2y(y+15)-117=0

We multiply parentheses

2y^2+30y-117=0

a = 2; b = 30; c = -117;
Δ = b2-4ac
Δ = 302-4·2·(-117)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{51}}{2*2}=\frac{-30-6\sqrt{51}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{51}}{2*2}=\frac{-30+6\sqrt{51}}{4}
$