(3m-1)(3m-1)-12=0

Solution for (3m-1)(3m-1)-12=0 equation:

(3m-1)(3m-1)-12=0

We multiply parentheses ..

(+9m^2-3m-3m+1)-12=0

We get rid of parentheses

9m^2-3m-3m+1-12=0

We add all the numbers together, and all the variables

9m^2-6m-11=0

a = 9; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·9·(-11)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{3}}{2*9}=\frac{6-12\sqrt{3}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{3}}{2*9}=\frac{6+12\sqrt{3}}{18}
$