State tax filing

You will file a non-resident income tax return for Pennsylvania and a resident tax return for Delaware. 

You will report the same wages in both return. So you are not taxed twice, you are allowed a credit for the taxes paid to Pennsylvania. The net effect is that your overall state tax rate will be at the higher rate between the two states. If Delaware comes out to a higher amount, you will owe them money with your return. If Pennsylvania comes out as the higher rate, you will owe nothing to Delaware after filing that state’s return.

Make sure you complete the PA non-resident tax return first to get the credit on Delaware tax return. 

See : Delaware on Out of State Income