The good news is that "HP OfficeJet Pro 8720 All-in-one Printer" is listed as a supported printer. Additionally the 7th column shows that "Scan to PC" is also supported for this model.

Install HPLIP (HP Linux Imaging and Printing)

Open a terminal

(Although most things in Ubuntu can be done using a GUI interface, I'll list the commands because it's more expedient and also easier to document the exact steps).

Ensure you have the software repository enabled
```
sudo apt-add-repository universe
```
This will automatically update your repositories, but you can also execute sudo apt update to manually update, if needed.

Install HPLIP
```
sudo apt install hplip
```

Optionally, install HPLIP GUI tools
```
sudo apt install hplip-gui
```

Setup your printer (HP OfficeJet Pro 8720 All-in-one Printer)

Get your printer's network name

On your printer's LCD control panel, drag the gray top-bar down, tap the network icon, and write down the Host Name.

The network name may be something like "HP_OfficeJet_Pro_8720".

(You can use your printer's IP address, but I highly recommend setting up your printer using its network name, because IP addresses can change).

Setup HPLIP to use your printer

On your Ubuntu computer, execute the following command.

Replace "HP_OfficeJet_Pro_8720" with the actual network name of your printer from the previous step.

Be sure to add .local at the end, as shown!
```
sudo hp-setup -i HP_OfficeJet_Pro_8720.local
```

Supply the following information when requested:
- Please enter a name for this print queue (m=use model name:'psc_2500'*, q=quit) ?:
```
HP_8720_Printer
```
- Does this PPD file appear to be the correct one (y=yes*, n=no, q=quit) ?
```
y
```
- Enter a location description for this printer (q=quit) ?
  
  If you want to leave this blank, just press Enter
- Enter additional information or notes for this printer (q=quit) ?
```
HP OfficeJet Pro 8720 Printer
```
- Please enter a name for this fax queue (m=use model name:'psc_2500_fax'*, q=quit) ?
```
HP_8720_Fax
```
- Enter a location description for this printer (q=quit) ?
  
  If you want to leave this blank, just press Enter
- Enter additional information or notes for this printer (q=quit) ?
```
HP OfficeJet Pro 8720 Fax
```
- Would you like to perform fax header setup (y=yes*, n=no, q=quit) ?
```
n
```
- Would you like to print a test page (y=yes*, n=no, q=quit) ?
```
n
```

Make the printer default
1. In Ubuntu, open System Settings app
2. Select Printers in the left pane
3. Click the gear icon next to "HP_8720_Printer"
4. Check-mark "Use Printer by Default"

Test Scanning

Launch Simple Scan (aka. "Document Scanner")

Wait for "Searching for Scanners" to complete

You should see the message "Ready to Scan"

Select "HP HP_OfficeJet_Pro_8720" from the drop down

Click the Scan button in the header bar