24m^2-14m-16=0

Solution for 24m^2-14m-16=0 equation:

24m^2-14m-16=0

a = 24; b = -14; c = -16;
Δ = b2-4ac
Δ = -142-4·24·(-16)
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{433}}{2*24}=\frac{14-2\sqrt{433}}{48}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{433}}{2*24}=\frac{14+2\sqrt{433}}{48}
$