a^2+6a-82=8

Solution for a^2+6a-82=8 equation:

a^2+6a-82=8

We move all terms to the left:

a^2+6a-82-(8)=0

We add all the numbers together, and all the variables

a^2+6a-90=0

a = 1; b = 6; c = -90;
Δ = b2-4ac
Δ = 62-4·1·(-90)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*1}=\frac{-6-6\sqrt{11}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*1}=\frac{-6+6\sqrt{11}}{2}
$