You can simply setup your streaming account to automatically push your live stream to your Facebook Page / Timeline by following those steps:
- Login your video streaming control panel and click on the "Stream Targets" button
- Click on " Create new stream target"
- If you like to give your stream a title and description, live the "Send a continuous live stream" option unchecked and click the "Continue with Facebook" button to authenticate with your Facebook account.
For better results we recommend you follow the Facebook streaming guides at https://developers.facebook.com/docs/videos/live-video/best-practices