To remove /wordpress from your site URL there are two steps needed, the first of which is to change the site URL for the install. To do this login to the wp-admin backend for the site and then go to Settings > General:
From the subsequent page you can then update the two URL's to remove /wordpress from the URL, once done and saved the site will cease to load in the short-term:
To get the site back online you will then need to move all site files from the /wordpress folder directly into the public_html folder, this will then match the URL you have updated in the backend and the site will load by default on your domain.
*** This guide will work for changing the URL to remove any folder name, /wordpress is just the example chosen to illustrate the process. ***
