x^2-31=7x+13

Solution for x^2-31=7x+13 equation:

x^2-31=7x+13

We move all terms to the left:

x^2-31-(7x+13)=0

We get rid of parentheses

x^2-7x-13-31=0

We add all the numbers together, and all the variables

x^2-7x-44=0

a = 1; b = -7; c = -44;
Δ = b2-4ac
Δ = -72-4·1·(-44)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-15}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+15}{2*1}=\frac{22}{2}
=11
$