The advice below is pretty much on target. HomeVestors is actually a franchise, but as far as purchasing homes they operate similar to other investors. The investor formula for making offers on homes is to take the ARV (after repair value) of a home, multiply that by 70%, then subtract needed repairs. So, for instance, if your home would sell for $500,000 after fix-up, an investor would multiply that number by 70%, resulting in a figure of $350,000. From that, the investor would subtract repairs and upgrades. Let's say $25,000 (paint, carpet, new baths, a bit of landscaping). So the MAO (maximum allowable offer) from an investor for the property would be $325,000. And that is taking a big hit to your equity. Sometimes that makes sense. Often, it doesn't. Is it "fair"? Depends on your needs and motivation.
You're right not to want to be stuck with two mortgages. OK, so what do you do? You can make the purchase of the new home contingent on the sale of your current home. That weakens your offer considerably, but it does protect and you, in this slow market, it's a very prudent step.
You can also get a bit more creative. Pay for an option on the property. Offer to pay $x (I don't know, maybe $2,500) for a 90 day option on the property, to be credited toward the purchase price if you exercise your option. You'll forfeit the option if you decide not to purchase. Taking that route would give you the option period--in this case 90 days--to sell your home. And you'd only be putting $2,500 at risk if your home didn't sell. Now, even if that's a possibility, the sellers probably would come back and request a shorter option period (probably 60 days max) and maybe more option consideration. That's all open to negotiation.
There are other techniques I've heard about--that come highly recommended, though I haven't tried them myself--that can sell your home faster. A round-robin auction, accompanied by massive marketing, is said to work well. I spoke to a couple of investors just yesterday who have used that technique in Northern Virginia and Maryland. That takes about a month, and reportedly will bring in 90%-95% of what a standard listing with a good, competent Realtor will. So, you're probably still going to take a slight hit on your equity, but that technique has a pretty good chance of moving your house very quickly.
In any case, though, marketing and pricing are vital elements to selling your home.
Hope that helps.