Eventual and eventually mean ‘final(ly)’, ‘in the end’. We use them when we say that something happened after a long time, or a lot of work.

    The chess game lasted for three days. Androv was the eventual winner.
    The car didn’t want to start, but eventually I got it going.

Eventual(ly) is a ‘false friend’ for students who speak some European languages. We do not use it to talk about possibilities — things that mighi happen. For this meaning, use possible, perhaps, if, may, might etc.

    In our new house. I’d like to have a spare bedroom for possible visitors. (NOT . . . eventual visitors.)
    I’m not sure what I’ll do next year. I might go to America if I can find a job (NOT…Eventually I’ll go to America)