The laws in each state differ, but your registration is typically based on your "permanent" residence. In other words, if you're going to school in one state but will otherwise still maintain your parent's house as your official residence, you may not have to register your vehicle in Delaware. If, however, you're setting out on your own and are establishing your own address from this point forward, you'll likely need to get it registered in the new state. Regardless, you should research the laws in Delaware, since that's where you'll be spending most of your time and doing most of your driving.
You live and learn. At any rate, you live.