6m^2=72+24m

Solution for 6m^2=72+24m equation:

6m^2=72+24m

We move all terms to the left:

6m^2-(72+24m)=0

We add all the numbers together, and all the variables

6m^2-(24m+72)=0

We get rid of parentheses

6m^2-24m-72=0

a = 6; b = -24; c = -72;
Δ = b2-4ac
Δ = -242-4·6·(-72)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-48}{2*6}=\frac{-24}{12}
=-2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*6}=\frac{72}{12}
=6
$