Constantine X Doukas was an old man when he came to power in 1059 AD. He made the poor decision of trying to save money by disbanding local garrisons and militia, instead counting on agreements with mercenaries if the need of defense should arise. This didn't work out, and over the course of Constantine X's reign, the Byzantine empire lost territory to the Normans in Italy, the Bulgars in Bulgaria, the Seljuks in Turkey, and the Oghuz Turks in the Balkans.
These medium-sized gold coins were made of old remelted issues, and they often carry impurities in the form of silver, bits of copper, or electrum (a naturally occurring alloy of gold and silver). The Greek inscriptions read '+IhS IXS REX REGNANTINM' (Jesus Christ, king of kings') on the obverse (convex side), and 'KWN RAC? O DOVKAC' (Con[stantine] ???? Doukas) on the reverse (concave side). In David R. Sear's catalog of Byzantine coins, this type is found as #1847. Sometimes there's an X on the shaft of the standard, but this doesn't change value.
worn: $300 US dollars approximate catalog value
average circulated: $450
well preserved: $700
The coin in our main picture (upper left) comes from Roma Numismatics. It is a gorgeous specimen that sold for about $620 US dollars during a 2016 auction. Requester Sanan's coin (to the right) is not as nice as Roma's coin. Sanan's coin would probably sell to a collector for $350 to $400 and to a coin dealer for one-half those values.
The values above are rough guidelines - each of these old coin stands on its own merits. A coin might be extremely well preserved but holed and bent, which lowers value significantly. Or a coin may be well worn but well struck on a good flan without problems, which helps push the value higher.