The solutions to your function is correct.

The profit P is equal to zero when x=100 or x=10. You might be thinking in terms of linearity (thinking the amount you spend on advertising is directly proportional to profit) but given your function P the function is parabolic, not linear. You have to consider market research and labor costs for example, which sometimes don't break even. You can also think in terms of supply and demand (the usual relationship between how much you have and how much people want is not necessarily linear).