x^2-22x=-112

Solution for x^2-22x=-112 equation:

x^2-22x=-112

We move all terms to the left:

x^2-22x-(-112)=0

We add all the numbers together, and all the variables

x^2-22x+112=0

a = 1; b = -22; c = +112;
Δ = b2-4ac
Δ = -222-4·1·112
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6}{2*1}=\frac{28}{2}
=14
$