Hello!
I will work at the reception of a hotel so
I would like to know what expressions can be said to calm down a disgruntled customer?

See a translation

Usually apologizing and stating what you can do to help is good:
“I’m sorry to hear that you’re having a problem with _____. I can ____ (move your room, ask them to quiet down, etc).”
“Sorry to hear that. We can try _____ (asking them to leave, making you a new key, etc).”
“I apologize for the inconvenience. Give me one moment to ____ (change your reservation, reimburse you, etc) .” You can mix and match any of those and it’ll still sound fine.

At the end of it when it is fixed:
“Thank you so much for your patience.”
“Thank you for waiting so patiently.”
“I really appreciate your patience.” (If they were actually patient, of course)

If you can’t do much to fix it, then openness about that is good, too:
“I’m really sorry for the inconvenience, there’s not much I can do right now. I’ll contact _____ (my manager, maintenance) to see if there’s a way to fix that.”

If they’re really upset/being nasty:
“Sir/Ma’am, I can see you’re really upset, but we can only fix this if we’re both calm.”
“I know/understand this is really frustrating but I can’t do anything if we’re not both calm.”
“This is frustrating for both of us, but if we go about it like this we’re not going to get anything done.”
“I’d really like to help you, but I need you to calm down first.”

Sometimes people are just plain old awful so don’t forget to stick up for yourself if they’re being excessively rude! A customer that is really rude is probably not someone you want staying with you anyway🤷‍♂️