-16m^2+112m+144=0

Solution for -16m^2+112m+144=0 equation:

-16m^2+112m+144=0

a = -16; b = 112; c = +144;
Δ = b2-4ac
Δ = 1122-4·(-16)·144
Δ = 21760
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:

$\sqrt{\Delta}=\sqrt{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-16\sqrt{85}}{2*-16}=\frac{-112-16\sqrt{85}}{-32}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+16\sqrt{85}}{2*-16}=\frac{-112+16\sqrt{85}}{-32}
$