The quickest (39 hours) and shortest (2704 miles) way is to go from Los Angeles to Barstow and take I-40 through NeedlesFlagstaffPetrified Forest National ParkAlbuquerqueAmarillo to Oklahoma City and then take I-44 to Tulsa and St. Louis.  Then I-70 to Indianapolis and Columbus and Harrisburg to Wilmington (Delaware)

It would be a hour longer to deviate a little bit when you get to St. Louis and take I-64 to Louisville and Lexington and Charleston (West Virginia) and then take I-79 up to Morgantown and then take I-68 through Sideling Hill to Baltimore and then go up I-95 to Wilmington.  I would prefer to visit Louisville rather than Indianapolis, but I also don't particularly care for I-95

The same time but a little more distance would have you go on a more northern route I-15 from Las Vegas and switch to I-70 to Grand Junction and Denver  Then I-76 up to North Platte and I-80 through Omaha Des Moines and Chicago Then I-90 to Cleveland and Pittsburgh at which point you would be going to Harrisburg and then to Wilmington.