For an analytic solution of this quartic:
Solve[x^4 - 2 x^3 - 9 x^2 - 3 x - 1 == 0, x, Quartics -> True]
or for a numerical version
N[Solve[x^4 - 2 x^3 - 9 x^2 - 3 x - 1 == 0, x]]
