Cadd9 ------------->  F7b5

C, E, G, D --------------->  F, Ab/G#, C, Eb/D#

the tension of C resolves to C

the tension of E resolves to F 

the tension of G resolves to Ab

the tension of D resolves to Eb

First off, F7b5 is a dominant chord: a major chord with a minor seventh.
The b refers to the following interval, ie 5. That interval is lowered 1/2-step.
-> F-A-Cb-Eb

Second, sharps and flats are not interchangeable. A third up from F is always going to have the letter A associated with it, and an ascending seventh will have an E-related note
-> the chord you thought was actually F-Ab-C-Eb only

Finally, please give the context. I'm not convinced of there actually being resolution of dominant sevenths outside rock-and-roll/blues-oriented genres (moreover, you wrote an add9 instead)
The question is, which one of the chords sounds more tense? Does the tension resolve or does it actually increase? What you are talking about is voice leading, not necessarily resolving tension.

Also, F Ab C Eb is Fm7.

If we are in the key of C, Cadd9 sounds very stable so there's really no tension to be resolved. But in some other key Cadd9 may sound pretty unstable. It has to do with the context.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.


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And some guitarists still produce their tensions in the good old
fashioned way, by losing track of where they are in the song.
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