-x2+22x+112=0

Solution for -x2+22x+112=0 equation:

-x2+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 = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{233}}{2*-1}=\frac{-22-2\sqrt{233}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{233}}{2*-1}=\frac{-22+2\sqrt{233}}{-2}
$