In our books we set a budget for the whole year. We purchased a camera in full which was in the budget. I want to show it in fixed assest to show in the balance sheet and expense it to reflect the budget... is this possible
What would be the correct way

You can't do both. If the camera is expensive enough (i.e. material enough) to be considered a fixed asset, then it should have been in the budgeted balance sheet, not on the budgeted income statement. That is, the budget should be reflecting how it's really going to happen. If you aren't planning to expense the camera, then you don't budget it as an expense.

Regardless, you can't put it both places. It's either an asset or it's an expense. I can't tell you where it "should" be because I don't know if it's something you need to capitalize. If it's material enough, then it should be. If it's something cheaper, it's up to you. Companies usually have guidelines about what dollar amount it takes before capitalizing something, and that will depend on the size of the company. ($500 in a very small company would likely mean capitalizing it, whereas that's nothing to a place like GM.)(Maybe I should start using a different example besides GM. :p)

Decide where to put it based on proper accounting logic, not on how you did it in the budget. If it was wrong in the budget, then work on how to do a budget. Don't record something just to make it "fit" a budget. Doesn't work that way.

(You also might want to consider the difference between a budgeted income statement and a budgeted cash flow. Were you actually doing a budgeted cash flow? That's not all expenses.)