9m^2+2m=12

Solution for 9m^2+2m=12 equation:

9m^2+2m=12

We move all terms to the left:

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

a = 9; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·9·(-12)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{109}}{2*9}=\frac{-2-2\sqrt{109}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{109}}{2*9}=\frac{-2+2\sqrt{109}}{18}
$