54m+6m^2-48=0

Solution for 54m+6m^2-48=0 equation:

54m+6m^2-48=0

a = 6; b = 54; c = -48;
Δ = b2-4ac
Δ = 542-4·6·(-48)
Δ = 4068
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:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{113}}{2*6}=\frac{-54-6\sqrt{113}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{113}}{2*6}=\frac{-54+6\sqrt{113}}{12}
$