X^2-18x-19=31

Solution for X^2-18x-19=31 equation:

X^2-18X-19=31

We move all terms to the left:

X^2-18X-19-(31)=0

We add all the numbers together, and all the variables

X^2-18X-50=0

a = 1; b = -18; c = -50;
Δ = b2-4ac
Δ = -182-4·1·(-50)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{131}}{2*1}=\frac{18-2\sqrt{131}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{131}}{2*1}=\frac{18+2\sqrt{131}}{2}
$