112=6x+x^2

Solution for 112=6x+x^2 equation:

112=6x+x^2

We move all terms to the left:

112-(6x+x^2)=0

We get rid of parentheses

-x^2-6x+112=0

We add all the numbers together, and all the variables

-1x^2-6x+112=0

a = -1; b = -6; c = +112;
Δ = b2-4ac
Δ = -62-4·(-1)·112
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-22}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+22}{2*-1}=\frac{28}{-2}
=-14
$