formal way of saying "I want to"

Actually, I want to know is perfectly valid. If it’s politeness you’re trying to achieve, you could say I would like to know.

This transforms what might have been interpreted as a demand into a request.

An alternative word would be enquire, such as in I would like to enquire.

You can precede to know with all sorts of verbs. Which you choose depends on the context, and the precise degree of formality and politeness you are striving for. In many contexts, including formal ones, I want to know may well serve the purpose, but occasionally you may, for example, want to write I should like to know. It’s really not possible to say more than that without knowing the purpose of the text you have in mind.

Alternative expression for I want to know could be something like I enquire, I seek, I investigate, etc.

There’re lots of ways to say it, but you may have to decide which suits you best based on your actual context.