I don't have a delete button when I go to Settings, choose Calendars, etc. then my gmail account I want to delete on my work iPad. I see only a sign-out option. Do I have to have my work delete my personal gmail account since they are the main account holder.
If you go into settings -> mail, Contacts, Calendars all of your accounts should be listed there. (Your question does not mention that specific location, did you go there?) Tap on the one you want to delete and scroll to the bottom of the screen. There should be an option to to remove the account.
Depending on how the iPad was set up at work they may have some sort of MDM installed that prevents you from doing a number of things, including adding or removing accounts and apps, changing certain settings and the like. If that is the case you may have to talk with your IT people to do what you want to do.