4m^2-24m+36=12

Solution for 4m^2-24m+36=12 equation:

4m^2-24m+36=12

We move all terms to the left:

4m^2-24m+36-(12)=0

We add all the numbers together, and all the variables

4m^2-24m+24=0

a = 4; b = -24; c = +24;
Δ = b2-4ac
Δ = -242-4·4·24
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{3}}{2*4}=\frac{24-8\sqrt{3}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{3}}{2*4}=\frac{24+8\sqrt{3}}{8}
$