24k^2-20k-32=0

Solution for 24k^2-20k-32=0 equation:

24k^2-20k-32=0

a = 24; b = -20; c = -32;
Δ = b2-4ac
Δ = -202-4·24·(-32)
Δ = 3472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{217}}{2*24}=\frac{20-4\sqrt{217}}{48}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{217}}{2*24}=\frac{20+4\sqrt{217}}{48}
$