If you had entered a relationship, without giving up anything, then, when you discover the adultery you have a back stop. Your life, sans your relationship, exists.
If you have nothing but the relationship, you can’t just walk onto an empty path.
You might want to flee into the night, but it makes no sense.
You need to wait until you are healed.
Take the revelation of adultery as you would a high impact accident which puts you in the hospital.
You have to heal, you have to rehabilitate.
You need time.
If the adulterer asks for time, give it. Asks for a second chance, give it. Do everything you can to keep the situation as it was before the revelation.
And then, work out your escape plan.