How to exclude weekend days from a date formula field

If you need the result to be a Work Date field type due to using Predecessors, then it would need to be

ToWorkDate(WeekdayAdd([Start Date],0))

First one worked perfectly, 2nd one gave me an error. But now I'm trying to filter out holidays for my Estimated Started Date (which was just a Work Date formula field, [Start Date with Check]} and tried this calc to add a day after the holidays and this didn't work: 
If([Start Date with Check]=ToDate("01-01-2018"),WeekdayAdd([Start Date with Check],1),
[Start Date with Check]) 

yikes I'm off somewhere again! :(

When  you say that it did not work,  was there a syntax error or you did not get there result that you expected?

There was a syntax error.  It says the function is defined to be ToWorkDate (Date d).
The Start Date field is already a Work Date field and the Start Date with Check formula field is a Work Date field so maybe I don't need to add the ToWorkDate?

Right, if they are already Workdate field types, then you do not need to convert them to Work Dates.   

But a "work date" field type is actually an unusual field type and only used with predecessors.  If you don't know about predecessors, it sounds like you may have got yourself all tangled up needlessly in Work Date field types and you should not be using Work Date formuals at all.

I am using predecessors. :)