x^2+6x-86=8

Solution for x^2+6x-86=8 equation:

x^2+6x-86=8

We move all terms to the left:

x^2+6x-86-(8)=0

We add all the numbers together, and all the variables

x^2+6x-94=0

a = 1; b = 6; c = -94;
Δ = b2-4ac
Δ = 62-4·1·(-94)
Δ = 412
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{103}}{2*1}=\frac{-6-2\sqrt{103}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{103}}{2*1}=\frac{-6+2\sqrt{103}}{2}
$