-m^2+6m=-112

Solution for -m^2+6m=-112 equation:

-m^2+6m=-112

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1m^2+6m+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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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