Comment #14 on issue 1868 by Vinzent.Steinberg: solve(floating point, x) stopped working
http://code.google.com/p/sympy/issues/detail?id=1868
AFAIK, there exists a general solution for quartic equations. For polynomials of a higher degree than 4 it is proofed that no general solution exists. Quoting Wikipedia:
" Formulas for expressing the roots of polynomials of degree 2 in terms of square roots have been known since ancient times (see quadratic equation), and for polynomials of degree 3 or 4 similar formulas (using cube roots in addition to square roots) were found in the 16th century (see Niccolo Fontana Tartaglia, Lodovico Ferrari, Gerolamo Cardano, and Vieta). But formulas for degree 5 eluded researchers. In 1824, Niels Henrik Abel proved the striking result that there can be no general (finite) formula, involving only arithmetic operations and radicals, that expresses the roots of a polynomial of degree 5 or greater in terms of its coefficients (see Abel-Ruffini theorem). This result marked the start of Galois theory which engages in a detailed study of relationships among roots of polynomials."
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