While installing Joomla 3.x in our cPanel shared hosting accounts most probably, in the installation process, the installation script will alert you about the php configuration "Magic Quotes GPC" is enabled and joomla 3.x need this php variable disabled.
To resolve this problem and install joomla 3.x without problem you have to simply create or edit the file named .htaccess using a text editor in your computer (like notepad) and add the following line into it:
<IfModule lsapi_module> php_flag magic_quotes_gpc = Off </IfModule>
Then save the file and upload it in the directory where you are installing Joomla 3.x and also in the administrator directory.
This should resolve the problem and the installation scripts should let you install joomla 3.x without problem.
This will also correct an issue when quotes are escaped with slashes when you publish your articles.