-12m+4=6m^2-20

Solution for -12m+4=6m^2-20 equation:

-12m+4=6m^2-20

We move all terms to the left:

-12m+4-(6m^2-20)=0

We get rid of parentheses

-6m^2-12m+20+4=0

We add all the numbers together, and all the variables

-6m^2-12m+24=0

a = -6; b = -12; c = +24;
Δ = b2-4ac
Δ = -122-4·(-6)·24
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*-6}=\frac{12-12\sqrt{5}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*-6}=\frac{12+12\sqrt{5}}{-12}
$