3m(m-1)=m+9

Solution for 3m(m-1)=m+9 equation:

3m(m-1)=m+9

We move all terms to the left:

3m(m-1)-(m+9)=0

We multiply parentheses

3m^2-3m-(m+9)=0

We get rid of parentheses

3m^2-3m-m-9=0

We add all the numbers together, and all the variables

3m^2-4m-9=0

a = 3; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·3·(-9)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{31}}{2*3}=\frac{4-2\sqrt{31}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{31}}{2*3}=\frac{4+2\sqrt{31}}{6}
$