Question 339039
It would be tedious to guess and check so we will use the discriminant.

The discriminant for a cubic is considerably longer than that for a quadratic.

It is:

{{{b^2*c^2-4ac^3-4b^3d-27a^2d^2+18abcd}}}

In order for there to be three real roots, the discriminant must be > 0.

Letting {{{a=-2}}} {{{b=-4}}} {{{c=12}}} {{{d=20-k}}}, and

making the subs it whittles down to

{{{-108k^2+2916k>0}}}

{{{k(k-27)<0}}}

{{{k<27}}}

It has three real roots if k is less than 27.