IF Statement in Conditional Formula Expression

IF Statement in Conditional Formula Expression

I have looked at all the forums and support docs and still am having trouble with this.

Currently I have several formula fields that calculate a discount based on the input of the general price.

Here is an example of the current working formula expression:

((General_Ticket_Price  *  0.1  -  General_Ticket_Price)  *  -1)

But now I have a request to have different discounts based on the type of event. For instance IF input.event_type == "workshop" there would a different formula expression than IF  input.event_type == "class".

I have tried numerous ways to get this statement into the formula expression and always get the message  Your expression is not valid, please check the syntax.

Does anyone have the valid syntax to do this?