-6m(1-m)=9-2m

Solution for -6m(1-m)=9-2m equation:

-6m(1-m)=9-2m

We move all terms to the left:

-6m(1-m)-(9-2m)=0

We add all the numbers together, and all the variables

-6m(-1m+1)-(-2m+9)=0

We multiply parentheses

6m^2-6m-(-2m+9)=0

We get rid of parentheses

6m^2-6m+2m-9=0

We add all the numbers together, and all the variables

6m^2-4m-9=0

a = 6; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·6·(-9)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{58}}{2*6}=\frac{4-2\sqrt{58}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{58}}{2*6}=\frac{4+2\sqrt{58}}{12}
$