x^2-4x-31=-2x+25

Solution for x^2-4x-31=-2x+25 equation:

x^2-4x-31=-2x+25

We move all terms to the left:

x^2-4x-31-(-2x+25)=0

We get rid of parentheses

x^2-4x+2x-25-31=0

We add all the numbers together, and all the variables

x^2-2x-56=0

a = 1; b = -2; c = -56;
Δ = b2-4ac
Δ = -22-4·1·(-56)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{57}}{2*1}=\frac{2-2\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{57}}{2*1}=\frac{2+2\sqrt{57}}{2}
$