12k^2-8k-24=0

Solution for 12k^2-8k-24=0 equation:

12k^2-8k-24=0

a = 12; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·12·(-24)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{19}}{2*12}=\frac{8-8\sqrt{19}}{24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{19}}{2*12}=\frac{8+8\sqrt{19}}{24}
$