Depending on how fast you can produce the required documents and your lender can process them a home equity mortgage loan can be closed in as little as one week. Most home equity loans take two to three weeks to get the cash.
If two to three weeks is not fast enough you are likely in an emergency situation, knew you needed the money and procrastinated or are being scammed by a pushy sales person. If you are the last person, you should seriously consider if you really need to make the purchase with your homes equity and in such a short time frame.
If you are insistent on closing your home equity loan as soon as possible you should seek lenders who specialize in home equity loans and more prepared to get everything right the first time with a streamlined process.