I'm not in the jewelry business, but...
There are 20 "pennyweights" to the troy ounce.
The price you always see quoted for gold is the price per troy ounce. A troy ounce is a bit larger than a "regular" ounce.
Your 14 karat gold ring is 14/24 = 58.333% "pure" gold.
If the total weight of the ring is 7.9 pennyweights, it is 0.395 ounces.
The gold content of the ring is 0.395 * .58333 = .2304 troy ounces of gold.
.2304 oz. * 1128 per oz. = Approximately $260 is the "melt value" of your ring.
Of course, any place you sell to has to make a bit of profit, you'd never get $260 for it.
The highest price I've seen offered in print is $20.50 per pennyweight of 14K gold, which would translate to about $162 for your ring. But that was a month or so ago, and the price of gold has risen since then.
I wouldn't take less than $175 for it.
Maybe try a coin shop - some of them buy scrap gold.