I made my first game in unity, and I was wondering if I can sell it without owing anything to unity?
From the Unity FAQ:
This is also mentioned in the Unity Software License Agreement. Note that Software refers to the Unity software. The game or application you are creating is the Licensee Content (See section 13. Definitions). The section quoted in the other answer tells you that you can't distribute the trial or educational versions of their software runtime. With other versions, you may distribute the software bundled with the game you created.
No, they don't own your game.
But they do own their engine. In Unity's EULA you can find relevant information about how the license between the developer and Unity works out.