2x^2-8x=91

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

2x^2-8x=91

We move all terms to the left:

2x^2-8x-(91)=0

a = 2; b = -8; c = -91;
Δ = b2-4ac
Δ = -82-4·2·(-91)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{22}}{2*2}=\frac{8-6\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{22}}{2*2}=\frac{8+6\sqrt{22}}{4}
$