y^2+8y=-5

Solution for y^2+8y=-5 equation:

y^2+8y=-5

We move all terms to the left:

y^2+8y-(-5)=0

We add all the numbers together, and all the variables

y^2+8y+5=0

a = 1; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·1·5
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{11}}{2*1}=\frac{-8-2\sqrt{11}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{11}}{2*1}=\frac{-8+2\sqrt{11}}{2}
$