Not gonna happen
First, the only quick way to raise fico score is to lower your credit balance to limit ratio below 35%. Other than this – it takes time.
Second, paying of the collection WON’T improve your score. The damage is already done. The collection will remain on your credit report for 7.5 years. The only thing you CAN do by paying off is to change its status from Unpaid to Paid or Settled. It won’t improve your FICO score, but creditor and lenders (including car dealers) do look at your credit report, and a paid collection does look much better than unpaid one (See why-pay-off-debts.html for more information).
As to the score itself – I believe that the Equifax score is a bit different from FICO. In any case, the score you see when you check it online is completely different than what your car dealers see on his system.