How long into pregnancy will a home test show a positive answer?

I haven’t had a period for almost two months now. So last week i took two pregnancy tests. One came up negative, but the other one showed a positive result, but was invalid because the line in the second window (that shows up to show that the test worked) never showed up. There is a good possibility im pregnant, but I’m not sure and honestly don’t want to believe I am. How long should it take for a home pregnancy test to say positive?