You need to install a server based in RTMP solution, they are many out there, Wowza to start is good give you 30 day test.
In this server you need to use a Caputer Card, can be use Intensity pro from blackmagic only 1 channel for stream out.
Software you need:
FFmpeg with x264 Plugin
The Internet you have is where you will be in problem just for let you know they KEY on streaming is the UPLOAD, download is nothing.
HD Channel is from 9Mbps to 4 mbps
SD Channel is from 2.3 to 2.9 mbps
So with ffmpeg you need to lower the bitrate at least 900kb so you can be able stream out the stream properly, but you can't have cleint conected only 1, becuase your uplaod, If you are looking to stream out to clients then you need to Push this stream to a 3party CDN company they are many out there .
You would be lucky to be able to encode more than 1 or 2 streams in realtime on that very old hardware. For just one transcoding instance (one stream in, many out) it might work at SD quality, or just serving VOD with pre-encoded content, but I doubt it could encode HD content in realtime without GPU assistance.
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