a^2+8a=-6

Solution for a^2+8a=-6 equation:

a^2+8a=-6

We move all terms to the left:

a^2+8a-(-6)=0

We add all the numbers together, and all the variables

a^2+8a+6=0

a = 1; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·1·6
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*1}=\frac{-8-2\sqrt{10}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*1}=\frac{-8+2\sqrt{10}}{2}
$