IF ISBLANK and NOT

I can't swear I followed all of your logic, but here's a formula that appeared to work as I understood it. If I got one of the conditions backwards, you should be able to change it. A couple of things to note:

I used the function WEEKDAY to determine whether the date in column C is a Sat or Sun.

I used the comparator <> to mean "not equal"

So one part of the formula reads this way in order to return "TRUE" if the date is neither Sunday (1) or Saturday (7)

AND(......WEEKDAY(C10,1)<>1),WEEKDAY(C10,1)<>7)

The complete formula, then, is simply

=IF(AND(ISBLANK(X10),WEEKDAY(C10,1)<>1,WEEKDAY(C10,1)<>7),$X$6,0)

Note, I did the testing in row 10 of my spreadsheet.

(For future reference, if you could actually attach a spreadsheet, or include a link to it on a shared drive, that would provide more incentive for people to help. Otherwise, you're kind of forcing us to create our own. Any actual that you provide should not include proprietary or confidential info, but in this case it should be fairly easy for you to create what you've described.)