1. In reality, I didn't pass the exam.
2. The fact is that I didn't pass the exam.
1 is grammatically correct, but number 2 is more common and sounds more natural.
You can use this to bring conversation back to the *facts*, if you think that you or your partner have been talking too much about ideas or dreams.
I do not think there are any other ways to say exactly this in English.
In English you "take an exam". When you take an exam you may "pass" or "fail". For example:
"I've taken the exam three times, but I failed each time"
"I took the exam and passed"
"I've taken the exam, but I will only know next week if I passed or failed"
So you could use 1. Past Simple tense or 2. Present Perfect tense
1) The fact is that I didn't pass the exam
2) The fact is that I haven't passed the exam
1 means that you took the exam but failed. 2 means that you have never taken the exam, perhaps you hope to take it in the future.