If you try to delete the first default database created when exchange 2010 is installed chances are that you will not be able to do that even through the database does not have any user's on it.
But having said that the databases will contain 3 hidden mailboxes or "Arbitration" mailboxes which you will have to move over to a different database and only after that you can do ahead and delete the default database.
Ok now that I have ur mind running in circles lets get down to performing this action.
From the Exchange Management Shell run the below command
Get-mailbox -database <database name> -Arbitration
You will see the 3 hidden mailboxes...
Now create a new database and move these off the default database..
Get-mailbox -database <database name> -Arbitration | new-moverequest -targetdatabase <database name>
Once the move is complete you can now delete the default database!!