Finding the value of k that satisfies the discrimant

Question

I am struggling to do this question

Find the valus of $k$ so that $kx^2-2+kx+x=0$ has discriminant $Δ= -24$

I tried to use the formula $b^2-4ac$ but my answer is completely wrong.

Any ideas would be much appreciated

Answer 1

$$kx^2-2+kx+x=0\implies kx^2+(k+1)x-2=0$$ Then solve for: $b^2-4ac=-24$ for $a=k,b=k+1,c=-2$