As UJ95x and skidmark mentioned, there are 2 real ways to view the shows stored on your phone to your tv. The Moto X has Miracast built-in but your tv either has to be Miracast capable or have a Miracast dongle plugged into your tv's HDMI port. The second method is via Chromecast. Chromecast works via a limited number of apps (YouTube, Netflix or Google Play Movies/Music) from your phone/tablet. Chromecast is also a dongle that plugs into your tv's HDMI port.
There is also another way, but it requres:
1) A HDMI cord.
2) A HDMI > Mini USB adaptor.
Could play any video, picture, games, anything. But dongle is probably your best bet.