According to the rational root theorem, since the leading coefficient of the polynomial is 1, the real answer is a factor of 39. Try a few possible values, and we find that x=-3 works. Divide x+3 from (x^3-x^2+x+39), we have (x^2-4x+13). x^2-4x+13=0,
x^2-4x+4=-9,
(x-2)^2=-9
x-2=+-3i,
x=2+3i or 2-3i.
The roots are -3, 2+3i, 2-3i.