I need to transfer some Pokémon to Pokémon X from Pokémon Black to finish the national Pokédex and pet them. Is this possible or will this break both or one game? By the way, the games are both on the same platform.
You can trade Pokemon from Gen V games to Gen VI games, but not vice-versa. In order to do so, you need to enter the Hall of Fame in your Gen V game, and go to the PokeTransfer Lab on Route 15. In your Gen VI game, you need the Pokedex. You also must download Pokemon Bank and Pokemon Transporter. Choose which Pokemon you want to transfer to the Gen VI game, and place them in Box 1. Move any Pokemon you don't want to transfer out of Box 1. After this, use Poke Transporter, and follow the steps from there.
If you want to trade Pokemon from a Gen VI game to a Gen V game, you can't sorry. It's a one way process.
Hope I helped!