24k^2-8k-120=0

Solution for 24k^2-8k-120=0 equation:

24k^2-8k-120=0

a = 24; b = -8; c = -120;
Δ = b2-4ac
Δ = -82-4·24·(-120)
Δ = 11584
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:

$\sqrt{\Delta}=\sqrt{11584}=\sqrt{64*181}=\sqrt{64}*\sqrt{181}=8\sqrt{181}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{181}}{2*24}=\frac{8-8\sqrt{181}}{48}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{181}}{2*24}=\frac{8+8\sqrt{181}}{48}
$