The way you've written that could be written as (x+3)^2 all divided by 2.
So to start with I'd multiply y by 2 to get rid of the fraction on the right. So now we have 2y = (x+3)^2
Then square root the 2y to get rid of the power on the right. So now we have Square Root of 2y = x+3
Then it's simply subtract 3 from each side. So x = Square Root 2y - 3 (Remember the - 3 is NOT in the square root. It's separate)
I'm not 100% certain this is correct. I was very good at rearranging formulas in my GCSE and I don't ever remember doing anything special when it came to handling powers and roots etc. You don't need to work it out or anything as far as I know. You are just rearranging.
If you tried working out the quadratic on the right you end up with 2y = x^2 + 6x + 9 and then it gets really messy. I'm pretty sure it's what I wrote up top.