y^2+8y=24

Solution for y^2+8y=24 equation:

y^2+8y=24

We move all terms to the left:

y^2+8y-(24)=0

a = 1; b = 8; c = -24;
Δ = b2-4ac
Δ = 82-4·1·(-24)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*1}=\frac{-8-4\sqrt{10}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*1}=\frac{-8+4\sqrt{10}}{2}
$