22x=x^2+112

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

22x=x^2+112

We move all terms to the left:

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

We get rid of parentheses

-x^2+22x-112=0

We add all the numbers together, and all the variables

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