8y+y^2=200

Solution for 8y+y^2=200 equation:

8y+y^2=200

We move all terms to the left:

8y+y^2-(200)=0

a = 1; b = 8; c = -200;
Δ = b2-4ac
Δ = 82-4·1·(-200)
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{-(8)-12\sqrt{6}}{2*1}=\frac{-8-12\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{6}}{2*1}=\frac{-8+12\sqrt{6}}{2}
$