I have an administrator account on my mac I don't need, and know the password but cannot delete it.
Go to System Preferences > Users & Grops > unlock padlock > click in + > Create a new Administrator Account.
Now, you can delete the other Administrator account.
Close actual Session > Open session with the new Admin account > Go to System Preferences > Users & Groups > unlock padlock >select old Admin Account > click in -
You need to create a new admin account to be able to delete another one.