3m(m-1)=5m+3-2m

Solution for 3m(m-1)=5m+3-2m equation:

3m(m-1)=5m+3-2m

We move all terms to the left:

3m(m-1)-(5m+3-2m)=0

We add all the numbers together, and all the variables

3m(m-1)-(3m+3)=0

We multiply parentheses

3m^2-3m-(3m+3)=0

We get rid of parentheses

3m^2-3m-3m-3=0

We add all the numbers together, and all the variables

3m^2-6m-3=0

a = 3; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·3·(-3)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*3}=\frac{6-6\sqrt{2}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*3}=\frac{6+6\sqrt{2}}{6}
$