X^2-2x-31=71

Solution for X^2-2x-31=71 equation:

X^2-2X-31=71

We move all terms to the left:

X^2-2X-31-(71)=0

We add all the numbers together, and all the variables

X^2-2X-102=0

a = 1; b = -2; c = -102;
Δ = b2-4ac
Δ = -22-4·1·(-102)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{103}}{2*1}=\frac{2-2\sqrt{103}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{103}}{2*1}=\frac{2+2\sqrt{103}}{2}
$