X^2-2x=66

Solution for X^2-2x=66 equation:

X^2-2X=66

We move all terms to the left:

X^2-2X-(66)=0

a = 1; b = -2; c = -66;
Δ = b2-4ac
Δ = -22-4·1·(-66)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{67}}{2*1}=\frac{2-2\sqrt{67}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{67}}{2*1}=\frac{2+2\sqrt{67}}{2}
$