There is only one real root, x=-0.39486 approx.
Rewrite the equation: x(x^2-5x+8)=-4; x=-4/(x^2-5x+8).
A graph of the function shows the root to be about -0.4, so put this value into the right-hand expression:
x=-0.3937... Now plug this value into expression, and we get: x=-0.39512... And so on. After repeating this exercise a few times we arrive at x=-0.3948586756.