M3-4m2+2m=-12

Solution for M3-4m2+2m=-12 equation:

3-4M^2+2M=-12

We move all terms to the left:

3-4M^2+2M-(-12)=0

We add all the numbers together, and all the variables

-4M^2+2M+15=0

a = -4; b = 2; c = +15;
Δ = b2-4ac
Δ = 22-4·(-4)·15
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*-4}=\frac{-2-2\sqrt{61}}{-8}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*-4}=\frac{-2+2\sqrt{61}}{-8}
$