y^2+2y+8=180

Solution for y^2+2y+8=180 equation:

y^2+2y+8=180

We move all terms to the left:

y^2+2y+8-(180)=0

We add all the numbers together, and all the variables

y^2+2y-172=0

a = 1; b = 2; c = -172;
Δ = b2-4ac
Δ = 22-4·1·(-172)
Δ = 692
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:

$\sqrt{\Delta}=\sqrt{692}=\sqrt{4*173}=\sqrt{4}*\sqrt{173}=2\sqrt{173}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{173}}{2*1}=\frac{-2-2\sqrt{173}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{173}}{2*1}=\frac{-2+2\sqrt{173}}{2}
$