6m^2-12m=6

Solution for 6m^2-12m=6 equation:

6m^2-12m=6

We move all terms to the left:

6m^2-12m-(6)=0

a = 6; b = -12; c = -6;
Δ = b2-4ac
Δ = -122-4·6·(-6)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*6}=\frac{12-12\sqrt{2}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*6}=\frac{12+12\sqrt{2}}{12}
$