X^2-2x=109

Solution for X^2-2x=109 equation:

X^2-2X=109

We move all terms to the left:

X^2-2X-(109)=0

a = 1; b = -2; c = -109;
Δ = b2-4ac
Δ = -22-4·1·(-109)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{110}}{2*1}=\frac{2-2\sqrt{110}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{110}}{2*1}=\frac{2+2\sqrt{110}}{2}
$