This question already has an answer here:
I have an image that is a 3x5 photo. We need to resize it to 12x15 and still need it to retain most, if not all, of it's image quality.
I do not have access to Photoshop, so I use Paint.NET. From what I've personally experienced, when re-sizing an image, I always lose quality. In this case, it's a very specific image and we need to make it larger and retain quality because it's all we have to go on for a project we are working on.