I try to solve the following expression:

Solve[100 - 20 x - 8 x^2 + x^3 == 0, {x}]

and get as output terms containing complicated expressions using the imaginary unit (highlight added by me).

Evaluating the solutions numerically, it shows that they are all appearantly real:

N[Solve[100 - 20 x - 8 x^2 + x^3 == 0, {x}], 50]

the imaginary part is 0. x 10^-50. A plot of the function also shows the real zeros at -3.8..., 2.8... and 8.9...:

Plot[100 - 20 x - 8 x^2 + x^3, {x, -10, 10}]

What can I do the have the result returned by Solve modified not to use complex numbers, but only square and cube roots?