After I got the determinant from a matrix this is what I was left with a cubic equation.
How can I work with this?
$-3k^3-k^2+5 = 0$
I have looked at various links and websites like this one
https://www.wikihow.com/Solve-a-Cubic-Equation
But nothing seems to work with this cubic.
You can try it in Wolfram Alpha.
https://www.wolframalpha.com/input/?i=%E2%88%923k%5E3+-k%5E2%2B5
This polynomial has a single real root which is approximately $1.0843$.
If I were you I would check my previous calculations.
Maybe you have a mistake there and that's why you get this
particular polynomial and not some "nicer" one.