I live in VA but work in DE.For DE I reported zero income and paid no taxes. Should i pay the taxes to DE and request a credit from VA for the income i earned from DE.

I live in VA but work in DE.I was under the impression i need to pay taxes to the state you live.My employer deducted VA taxes for the earned income and zero for delaware. So for VA i reported the entire income and for DE I reported zero income and paid no taxes. Should i pay the taxes to DE and request a credit from VA for the income i earned from DE?