Yes, you need to call Delta for a mileage upgrade. It should be 25,000 miles per person each way.
This is a good use of miles if you can find the upgrade. But beware, the fees could add up if you need to make changes depending on the exact rule of your ticket. When you call to ask about the upgrade, also ask about the exact fare rules.
If your specific flight does not have upgrades, you could ask for alternative routing that has upgrade inventory.
Also, by the way, if you were to switch to Y, it would be 15,000 miles instead of 25K. Not worth the cost.