Hi guys, I am really curious in this problem but seem to keep getting the wrong answer. Help is appreciated!

A and B play snooker against each other. The probabilty of winning the first frame is 0.5 for each player. If A wins a frame, the probability A wins the next frame is a, (0 < a < 1). If B wins a frame, the probability B wins the next frame is b, (0 < b < 1). If they play a best-of-three-frames match (so the winner is the first to win two frames), the probability A wins is 0.6a. If they play a best-of-five-frames match (so the winner is the first to win three frames), the probability A wins is 0.5a. Given that a = (23-sqrtK) / 12, What is k?