You can't delete the front page but you can create a static front page.
Pages http://en.support.wordpress.com/pages/ are static and are for content that rarely changes. They sit outside of the blog structure and you cannot post to multiple pages in any blog. There is only one main page for posts http://en.support.wordpress.com/posts/ in a blog and all posts will display on the main blog page. There is no way to exclude posts from the main posts (blog) page.
The front page of the blog by default will display your posts (not pages) http://en.support.wordpress.com/post-vs-page/ in reverse chronological order, with the most recently published post on top. If you do not want all the posts to show on the front page, then you can create a static front page “Welcome” for your site and a “Blog” page for posts.
If you choose a static front page then you have to create two pages as I said above. After you do that you go to > Settings > Reading and make the designation change and click “save changes”. http://en.support.wordpress.com/pages/front-page/