So your full-Kelly expected utility function would look like:
E[U(x)] = p1*ln(1+x*w1) + p2*ln(1+x*w2) + ... + (1-Σpi)*ln(1-x)
Where pi and wi correspond to the probability of and the payout for (net of initial bet ... so decimal odds -1) respectively for the ith outcome, and x corresponds to the percentage of bankroll.
Taking the first derivative wrt x and setting to 0 gives us:
Σ [piwi/(1+xwi)] = (1-Σpi)/(1-x)
Which for n discrete outcomes yields an (n-1)th degree polynomial.
Anyway, attached is a simple spreadsheet that demonstrates a solution using Excel Solver. Fields intended for editing are the probability and outcome columns and the Kelly multiplier cell.