How to delete original partition
Just because you can, doesn't mean you should.

Why not just back up your data and wipe the entire partition? I suppose if you want to learn how to move things around and you already have a bootable backup that you've tested, the plan of action you propose might be an interesting learning experience.

For anyone that's not sure they can pull off this, Apple posts supported instructions for a wipe and reinstall.


https://support.apple.com/kb/PH18869


It uses the Recovery Partition to perform the wipe. If you don't run caching server to keep fast access to the installer you downloaded, you can make a USB bootable drive to do the deed as well.


https://support.apple.com/en-us/HT201372


These are supported and designed to avoid human errors. Also, it ensures you get a clean partition table with a supported Recovery HD partition for ongoing maintenance and efficient management of OS X.