Hmm, assuming the plant is still pretty healthy and also not having the tank stocked yet then there should not be any real readings of anything, most likely its your tap water thats giving these readings as in the UK its pretty commin to have nitrate in the tap anything from 10 to 40ppm is usual.
As Akasha has already mentioned, a half decen test kit will prove invaluable for the new fishkeeper as this tests the water to ensure you tank water is safe for potential stocking in future. API master test kit are ok and a popular choice amongst keepers on this forum.
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Then I would urge you to start doing a 'Fishless Cycle' this basically means you are adding good bacteria to the tank and filter to make the water safer for fish.
Fish produces ammonia basically simply by being alive in the tank. Therefore this ammonia needs to be converted into nitrite then this nitrite needs to be converted into nitrate.
The only sure way of doing this is to cycle your tank to have the relevant bacterias needed to consume ammonia and making this ammonia into nitrite and then a different type of bacteria consumes this nitrite and produces nitrate.
All this ammonia, nitrite and nitrate are actually toxic to fish in varying degrees, so by doing this cycle this we are actually help to create a system that works for the fish you keep inside your tank.
The end result of this sytem is nitrate, as already mentioned, this can be toxic to fish, especially at high levels, so we fishkeepers do a once weekly water change of at least 25% but I would recommend 50%, this water change is what reduces the nitrate level to a safer level for the fish.
Live plants are a good additions in the sense they can consume some nitrate as well as ammonia so that is a nice bonus
i would recommend you to read this article, it will prove to be useful information to learn, its a lot to take in at first but given time and practical fishkeeping, you will surely begin to understand what all this mean.
Cycling Your New Fresh Water Tank: Read This First!
Our first priority in fishkeeping is the welfare of our fish, shrimps and inverts we choose to keep in our tanks.
Btw, if you do go ahead with doign a fishless cycle, then you will need a source of ammonia, we usually use a bottled ammonia, like Kleen Off or specially made ammonia for fishtank cycling, both these as well as other brands can easily be obtained online as well as the test kit already mentioned earlier.
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NOTE - these pictures are what I have used personally without any problems in the past, however, do not feel you have to purchase any of these and there are many other brands that are probably perfectly fine.