5k2-8k-16=0

Solution for 5k2-8k-16=0 equation:

5k^2-8k-16=0

a = 5; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·5·(-16)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{6}}{2*5}=\frac{8-8\sqrt{6}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{6}}{2*5}=\frac{8+8\sqrt{6}}{10}
$