6m(3m+21)=9

Solution for 6m(3m+21)=9 equation:

6m(3m+21)=9

We move all terms to the left:

6m(3m+21)-(9)=0

We multiply parentheses

18m^2+126m-9=0

a = 18; b = 126; c = -9;
Δ = b2-4ac
Δ = 1262-4·18·(-9)
Δ = 16524
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:

$\sqrt{\Delta}=\sqrt{16524}=\sqrt{324*51}=\sqrt{324}*\sqrt{51}=18\sqrt{51}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-18\sqrt{51}}{2*18}=\frac{-126-18\sqrt{51}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+18\sqrt{51}}{2*18}=\frac{-126+18\sqrt{51}}{36}
$