m^2-12m=-24

Solution for m^2-12m=-24 equation:

m^2-12m=-24

We move all terms to the left:

m^2-12m-(-24)=0

We add all the numbers together, and all the variables

m^2-12m+24=0

a = 1; b = -12; c = +24;
Δ = b2-4ac
Δ = -122-4·1·24
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*1}=\frac{12-4\sqrt{3}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*1}=\frac{12+4\sqrt{3}}{2}
$