8y+y^2=165

Solution for 8y+y^2=165 equation:

8y+y^2=165

We move all terms to the left:

8y+y^2-(165)=0

a = 1; b = 8; c = -165;
Δ = b2-4ac
Δ = 82-4·1·(-165)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{181}}{2*1}=\frac{-8-2\sqrt{181}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{181}}{2*1}=\frac{-8+2\sqrt{181}}{2}
$