0=6m^2-m-12

Solution for 0=6m^2-m-12 equation:

0=6m^2-m-12

We move all terms to the left:

0-(6m^2-m-12)=0

We add all the numbers together, and all the variables

-(6m^2-m-12)=0

We get rid of parentheses

-6m^2+m+12=0

a = -6; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-6)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-6}=\frac{16}{-12}
=-1+1/3
$