6m^2=13m+12

Solution for 6m^2=13m+12 equation:

6m^2=13m+12

We move all terms to the left:

6m^2-(13m+12)=0

We get rid of parentheses

6m^2-13m-12=0

a = 6; b = -13; c = -12;
Δ = b2-4ac
Δ = -132-4·6·(-12)
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{457}}{2*6}=\frac{13-\sqrt{457}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{457}}{2*6}=\frac{13+\sqrt{457}}{12}
$