a^2+6a=108

Solution for a^2+6a=108 equation:

a^2+6a=108

We move all terms to the left:

a^2+6a-(108)=0

a = 1; b = 6; c = -108;
Δ = b2-4ac
Δ = 62-4·1·(-108)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{13}}{2*1}=\frac{-6-6\sqrt{13}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{13}}{2*1}=\frac{-6+6\sqrt{13}}{2}
$