12m^2-1=-3m

Solution for 12m^2-1=-3m equation:

12m^2-1=-3m

We move all terms to the left:

12m^2-1-(-3m)=0

We get rid of parentheses

12m^2+3m-1=0

a = 12; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·12·(-1)
Δ = 57
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{-(3)-\sqrt{57}}{2*12}=\frac{-3-\sqrt{57}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*12}=\frac{-3+\sqrt{57}}{24}
$