6m^2-32=4m

Solution for 6m^2-32=4m equation:

6m^2-32=4m

We move all terms to the left:

6m^2-32-(4m)=0

a = 6; b = -4; c = -32;
Δ = b2-4ac
Δ = -42-4·6·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*6}=\frac{-24}{12}
=-2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*6}=\frac{32}{12}
=2+2/3
$