y^2+8y=-3

Solution for y^2+8y=-3 equation:

y^2+8y=-3

We move all terms to the left:

y^2+8y-(-3)=0

We add all the numbers together, and all the variables

y^2+8y+3=0

a = 1; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·1·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{13}}{2*1}=\frac{-8-2\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{13}}{2*1}=\frac{-8+2\sqrt{13}}{2}
$