12m^2-13=-6m

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

12m^2-13=-6m

We move all terms to the left:

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

We get rid of parentheses

12m^2+6m-13=0

a = 12; b = 6; c = -13;
Δ = b2-4ac
Δ = 62-4·12·(-13)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{165}}{2*12}=\frac{-6-2\sqrt{165}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{165}}{2*12}=\frac{-6+2\sqrt{165}}{24}
$