m^2=32m-192

Solution for m^2=32m-192 equation:

m^2=32m-192

We move all terms to the left:

m^2-(32m-192)=0

We get rid of parentheses

m^2-32m+192=0

a = 1; b = -32; c = +192;
Δ = b2-4ac
Δ = -322-4·1·192
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16}{2*1}=\frac{16}{2}
=8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16}{2*1}=\frac{48}{2}
=24
$