12m(3m+24)=9

Solution for 12m(3m+24)=9 equation:

12m(3m+24)=9

We move all terms to the left:

12m(3m+24)-(9)=0

We multiply parentheses

36m^2+288m-9=0

a = 36; b = 288; c = -9;
Δ = b2-4ac
Δ = 2882-4·36·(-9)
Δ = 84240
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:

$\sqrt{\Delta}=\sqrt{84240}=\sqrt{1296*65}=\sqrt{1296}*\sqrt{65}=36\sqrt{65}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-36\sqrt{65}}{2*36}=\frac{-288-36\sqrt{65}}{72}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+36\sqrt{65}}{2*36}=\frac{-288+36\sqrt{65}}{72}
$