Yes your computer is compatible with vega 64 . Follow directions you will need to read your manual and disable the onboard graphic card when u plug your graphic card to the pci express slot for it to send video from the vega 64. I recommend a pci express 8 pin adapter . This power supply will supply it just need adapter. Get yourself a dual 6pin female to 1x 8pin male
750-Watt Power Supply (Suggestion)
2 x 8-pin AUX Power Connector
64-bit operating system highly recommended
CD-ROM or DVD-ROM drive for installing software
PCI Express 2.0 or higher version based PC is required with one X16 lane graphics slot available on the motherboard in order for the card to be compatible with
The card needs 2 x 8 pin(150W ea.) pcie connections due to power requirement of card.
I do not know how the power from the HP PSU is distributed, but having only 6 pin cables(75W ea.) it's possible there is insufficient power capable of being routed to PCIE safely.
Ask HP support what the psu is capable of (and/or post a query on jonnyguru.com forum).