x^2-10x-31=-12

Solution for x^2-10x-31=-12 equation:

x^2-10x-31=-12

We move all terms to the left:

x^2-10x-31-(-12)=0

We add all the numbers together, and all the variables

x^2-10x-19=0

a = 1; b = -10; c = -19;
Δ = b2-4ac
Δ = -102-4·1·(-19)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{11}}{2*1}=\frac{10-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{11}}{2*1}=\frac{10+4\sqrt{11}}{2}
$