If you are single, there is an Exclusion of $250,00 of the gain on sale of primary residence (assuming you lived in the house 2 of the last 5 years). Thus, it is not true that there is an automatic deduction of $250,000 from the gross proceeds.
The real estate commission and other closing costs do get deducted. You start with the gross proceeds of $520,000 and then deduct the selling expenses and the you deduct your cost of the property plus all of the improvements (your cost plus the improvements are referred to as "Basis" in tax speak).
If you complete the calculations and your gain is $250,000, then you owe no tax on the sale.
Utah state income tax begins with Federal Adjusted Gross Income, so if gain is excluded for Federal income tax purposes, it does not affect your Utah income tax liability.
