5m^2-2m-12=6

Solution for 5m^2-2m-12=6 equation:

5m^2-2m-12=6

We move all terms to the left:

5m^2-2m-12-(6)=0

We add all the numbers together, and all the variables

5m^2-2m-18=0

a = 5; b = -2; c = -18;
Δ = b2-4ac
Δ = -22-4·5·(-18)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{91}}{2*5}=\frac{2-2\sqrt{91}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{91}}{2*5}=\frac{2+2\sqrt{91}}{10}
$