8k^2=-24k

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

8k^2=-24k

We move all terms to the left:

8k^2-(-24k)=0

We get rid of parentheses

8k^2+24k=0

a = 8; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·8·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*8}=\frac{-48}{16}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*8}=\frac{0}{16}
=0
$