-8k^2-56k-24=0

Solution for -8k^2-56k-24=0 equation:

-8k^2-56k-24=0

a = -8; b = -56; c = -24;
Δ = b2-4ac
Δ = -562-4·(-8)·(-24)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{37}}{2*-8}=\frac{56-8\sqrt{37}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{37}}{2*-8}=\frac{56+8\sqrt{37}}{-16}
$