12y+y^2=180

Solution for 12y+y^2=180 equation:

12y+y^2=180

We move all terms to the left:

12y+y^2-(180)=0

a = 1; b = 12; c = -180;
Δ = b2-4ac
Δ = 122-4·1·(-180)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*1}=\frac{-12-12\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*1}=\frac{-12+12\sqrt{6}}{2}
$