The formula is in many ways similar to French Roulette. Except a few things are different. Since there are 38 tiles in American Roulette, the probability to win is 1 in 38 and the probability to lose is 37 in 38. From then, this formula is derived:
-1 * 37/38 + 35 * 1/38 = -0.0526
From this final number, we can then derive the house advantage of American Roulette. -0.0526 = 5.26%.