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What version is this? I get with 6.8beta8
sage: b,c,d = var('b,c,d')
sage: Delta = (18*b*c*d - 4*b^3*d + b^2*c^2 - 4*c^3 - 27*d^2 == 0)
sage: solve(Delta,d)
[d == -2/27*b^3 + 1/3*b*c + 2/27*(b^2 - 3*c)^(3/2), d == -2/27*b^3 + 1/3*b*c - 2/27*(b^2 - 3*c)^(3/2)]
which is fine.
