I do not know how to solve this cubic equation. The background of this problem is from lagrange multiplier. I use lagrange multuplier to find the distance from point(m,n) to parabola. and I stuck with this step.
$$ x^3 - (2+2n)x^2 - (4n+1)x + (2m^2 - 2n) = 0 $$ when $m$ and $n$ are real numbers.
How to solve it?
Thank you.