3m^2-2m=6

Solution for 3m^2-2m=6 equation:

3m^2-2m=6

We move all terms to the left:

3m^2-2m-(6)=0

a = 3; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·3·(-6)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*3}=\frac{2-2\sqrt{19}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*3}=\frac{2+2\sqrt{19}}{6}
$