ContraDix Okay, so I must try to use this special terminal/console called TTS (using ctrl+alt+F2 when it freezes while booting Solus on Live Session) to update the live session while trying to boot.
That's not quite what I said, or at least, not quite what I meant. You need to boot the USB stick with the .ISO file on it, and then click an icon in the upper left corner that says something like "Install OS." Follow all the prompts, which will take you through a brief process of selecting the type of installation (tell it to use the whole disk), providing your location, your real name, your user name, and your password.
After you examine the page that shows what will be done, and verified that the information is all correct, you can click to install the OS. You need to confirm that a couple of times, because the next step will be to delete everything on the disk and write the contents of the .ISO file there.
At the end, you'll be instructed to reboot in order to use the new OS. It's a good idea at that point, instead of clicking on the [Restart] button, to just exit from the installer and shut down the live session. Then restart the computer. (That will make sure that the installer has written everything it needs to write to the disk.)
I don't remember if you told us which edition of Solus you're installing. In Budgie, there's a power icon in the system tray. In other editions, it's at the bottom of the "Start" menu.
When the computer boots up, you'll probably end up at the black screen we've mentioned, because the video driver it's looking for can't be found. That's when you press Ctrl+Alt+F2 to open a TTY terminal and invoke the sudo eopkg up commannd.
Sorry if I left any of this out of my explanation. I though I'd read that you have Solus running on another computer, so I may have believed you were more familiar with the process than you are. This should fill in any gaps in my previous explanation.