Indeed,
"cost about $50,000 after federal tax credits and generate $64,000 in energy over 30 years"
The tax credit is a 30% tax credit.
So the system costs $71,428.57, the homeowner gets a $21,428.57 credit so that the homeowners out of pocket is $50,000.
Overall the system is expected to produce benefits of $64,000.00
As a society we are still spending, in total, $71,428.57 to produce $64,000.00 worth of electricity.