-12m(m-10)=100

Solution for -12m(m-10)=100 equation:

-12m(m-10)=100

We move all terms to the left:

-12m(m-10)-(100)=0

We multiply parentheses

-12m^2+120m-100=0

a = -12; b = 120; c = -100;
Δ = b2-4ac
Δ = 1202-4·(-12)·(-100)
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{6}}{2*-12}=\frac{-120-40\sqrt{6}}{-24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{6}}{2*-12}=\frac{-120+40\sqrt{6}}{-24}
$