I have an image of 90x122 pixels i want to resize it to make it 512x512 pixels but the image loses it quality Is there any way of doing this without losing the quality?.
When you increase the size of an image (whether in Photoshop or any other program), the program has to add pixels. Since the information about what exactly what color those pixels should be doesn't exist in the original image, the program has to guess what it should add. There are different ways to make those guesses, but they are always nothing more than a guess, so the result will never have the same quality as a full-size original would have had.
It would be like taking a short story and applying a computer algorithm to expand it into a book. The computer might make some pretty good guesses, but the "book" is never going to read as well as one that was created in full by an author.
In either case, a skillful human (digital artist or author) can take the computer output and turn it in to something of good quality, but that's not something computer algorithms are currently capable of.
I assume that you tried the standard method already, with the best settings, and you are saying that result is missing "quality".
Depending on what you call quality, maybe the original image just does not have enough quality for an image in the larger size?
It could help if you add example images to explain the problem.