There's lots of discussion about wattages of power supplies and max TDP of video cards for you to research via google. Sounds like you'd be trying to put 10 pounds of flour in a 5 pound bag with the 75W 1050 Ti. it just has 2GB instead of 1GB DDR3 and draws a bit more power.

Per nVidia directly those use 41 vs 45W max TDP, and we don't see any better performance from the K620. We use the Quadro K600 or K620 cards in these without issue. you have a limit on the total 12V power from such a small power supply. HP has been sticking with the ATX standard for the PCIe x16 slot of it being able to provide 75W up to the card, but that is not the whole picture. You certainly can do better than those, from 2012. You can look on page 172 to see the cards HP certified at that time for the SFF Elite 8300. Business PCs, Workstations and Point of Sale Systems.Printer Wireless, Networking & Internet.DesignJet, Large Format Printers & Digital Press.Printing Errors or Lights & Stuck Print Jobs.Notebook Hardware and Upgrade Questions.The optional DVD+/-RW SuperMulti DL LightScribe drive makes your storage media stand-out with custom labels that you can burn directly to your disc, and also lets you record or watch DVDs and play CDs. Equipped with Intel® Core™2 Duo Processors and hard drives of up to 250-GB, this notebook features all the tools you need to carry out your business tasks quickly and efficiently.

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Select the right 15.4-inch diagonal WXGA display that best suits your needs-choose between the anti-glare or HP BrightView displays. Featuring genuine Windows for a familiar and intuitive environment With its fresh new look, impressive combination of mobile office features, the latest Intel® Core™2 Duo processor and a starting weight of only 5.5lbs/2.49kg, the HP Compaq 6720s is an excellent price-for-performance package.

The official marketing text of HP Compaq 6720s T8100 39.1 cm (15.4') Intel® Core™2 Duo 1 GB DDR2-SDRAM 120 GB Intel® GMA X3100 Windows Vista Business as supplied by the manufacturer

Hp compaq 6720s graphics card