X^2-2x=91

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

X^2-2X=91

We move all terms to the left:

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

a = 1; b = -2; c = -91;
Δ = b2-4ac
Δ = -22-4·1·(-91)
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{-(-2)-4\sqrt{23}}{2*1}=\frac{2-4\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{23}}{2*1}=\frac{2+4\sqrt{23}}{2}
$