8y+y^2=76

Solution for 8y+y^2=76 equation:

8y+y^2=76

We move all terms to the left:

8y+y^2-(76)=0

a = 1; b = 8; c = -76;
Δ = b2-4ac
Δ = 82-4·1·(-76)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{23}}{2*1}=\frac{-8-4\sqrt{23}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{23}}{2*1}=\frac{-8+4\sqrt{23}}{2}
$