-5k^2-22k-8=0

Solution for -5k^2-22k-8=0 equation:

-5k^2-22k-8=0

a = -5; b = -22; c = -8;
Δ = b2-4ac
Δ = -222-4·(-5)·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-18}{2*-5}=\frac{4}{-10}
=-2/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*-5}=\frac{40}{-10}
=-4
$