x = kb + a where kb + a > -1 is your general solution based upon your condition that x is not negative. Of course k could be any integer including even zero or a negative number for these conditions to be met.

Bear in mind that there could be no solutions at all. For example,
[tex]x^2 \equiv 2 \pmod 4[/tex]
has no solutions, since all squares modulo 4 are either 0 or 1.