(6m)^2-4*(1-m)*12=0

Solution for (6m)^2-4*(1-m)*12=0 equation:

(6m)^2-4(1-m)*12=0

We add all the numbers together, and all the variables

6m^2-4(-1m+1)*12=0

We multiply parentheses

6m^2+48m-48=0

a = 6; b = 48; c = -48;
Δ = b2-4ac
Δ = 482-4·6·(-48)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{6}}{2*6}=\frac{-48-24\sqrt{6}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{6}}{2*6}=\frac{-48+24\sqrt{6}}{12}
$