+ size - dpi = same quality?

I know this is very likely been asked before, but I don't know if it's the words or phrases I'm using or what but I can't find it. If it was resolved before, please just point me in the right direction.

I have to print a 20cm x 20cm image at 150dpi but the one I took with my camera is 10x10 at 300 dpi. (I'm using rounded numbers to make the example simpler)

Can I increase the size while sacrificing dpi and retain the same amount the quality? Is there a formular to calculate how much I can increase size per N dpi sacrificed? Can I do this in Photoshop?

Thanks