9m^2-125m=100

Solution for 9m^2-125m=100 equation:

9m^2-125m=100

We move all terms to the left:

9m^2-125m-(100)=0

a = 9; b = -125; c = -100;
Δ = b2-4ac
Δ = -1252-4·9·(-100)
Δ = 19225
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:

$\sqrt{\Delta}=\sqrt{19225}=\sqrt{25*769}=\sqrt{25}*\sqrt{769}=5\sqrt{769}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-5\sqrt{769}}{2*9}=\frac{125-5\sqrt{769}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+5\sqrt{769}}{2*9}=\frac{125+5\sqrt{769}}{18}
$