2(3m-4)6m=11

Solution for 2(3m-4)6m=11 equation:

2(3m-4)6m=11

We move all terms to the left:

2(3m-4)6m-(11)=0

We multiply parentheses

36m^2-48m-11=0

a = 36; b = -48; c = -11;
Δ = b2-4ac
Δ = -482-4·36·(-11)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-36\sqrt{3}}{2*36}=\frac{48-36\sqrt{3}}{72}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+36\sqrt{3}}{2*36}=\frac{48+36\sqrt{3}}{72}
$