5m^2-4m-24=0

Solution for 5m^2-4m-24=0 equation:

5m^2-4m-24=0

a = 5; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·5·(-24)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{31}}{2*5}=\frac{4-4\sqrt{31}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{31}}{2*5}=\frac{4+4\sqrt{31}}{10}
$