2x^2-2x=91

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

2x^2-2x=91

We move all terms to the left:

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

a = 2; b = -2; c = -91;
Δ = b2-4ac
Δ = -22-4·2·(-91)
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{183}}{2*2}=\frac{2-2\sqrt{183}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{183}}{2*2}=\frac{2+2\sqrt{183}}{4}
$