X^2-6x-91=-8

Solution for X^2-6x-91=-8 equation:

X^2-6X-91=-8

We move all terms to the left:

X^2-6X-91-(-8)=0

We add all the numbers together, and all the variables

X^2-6X-83=0

a = 1; b = -6; c = -83;
Δ = b2-4ac
Δ = -62-4·1·(-83)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{23}}{2*1}=\frac{6-4\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{23}}{2*1}=\frac{6+4\sqrt{23}}{2}
$