6m(2m+18)=4

Solution for 6m(2m+18)=4 equation:

6m(2m+18)=4

We move all terms to the left:

6m(2m+18)-(4)=0

We multiply parentheses

12m^2+108m-4=0

a = 12; b = 108; c = -4;
Δ = b2-4ac
Δ = 1082-4·12·(-4)
Δ = 11856
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:

$\sqrt{\Delta}=\sqrt{11856}=\sqrt{16*741}=\sqrt{16}*\sqrt{741}=4\sqrt{741}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{741}}{2*12}=\frac{-108-4\sqrt{741}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{741}}{2*12}=\frac{-108+4\sqrt{741}}{24}
$