Let G=S be a solvable permutation group given as input by generating set S. I.e.\ G is a solvable subgroup of the symmetric group Sn. We give a deterministic polynomial-time algorithm that computes an expanding generator set for G. More precisely, given a constant 1 we can compute an expanding generator set T of size n2(logn)O(1) such that the undirected Cayley graph Cay(GT) is a -spectral expander. In particular, this construction yields -bias spaces with improved size bounds for the groups Znd for any constant bias .