4m(m-2)=24

Solution for 4m(m-2)=24 equation:

4m(m-2)=24

We move all terms to the left:

4m(m-2)-(24)=0

We multiply parentheses

4m^2-8m-24=0

a = 4; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·4·(-24)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*4}=\frac{8-8\sqrt{7}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*4}=\frac{8+8\sqrt{7}}{8}
$