3m^2-39m=108

Solution for 3m^2-39m=108 equation:

3m^2-39m=108

We move all terms to the left:

3m^2-39m-(108)=0

a = 3; b = -39; c = -108;
Δ = b2-4ac
Δ = -392-4·3·(-108)
Δ = 2817
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:

$\sqrt{\Delta}=\sqrt{2817}=\sqrt{9*313}=\sqrt{9}*\sqrt{313}=3\sqrt{313}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{313}}{2*3}=\frac{39-3\sqrt{313}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{313}}{2*3}=\frac{39+3\sqrt{313}}{6}
$