Weed B Gon is a broad leaf "weed" poison and does not, or at least is not supposed to, affect grasses. If you want to kill the grass you need to find a poison that will do that.
Keep in mind that these poisons are having adverse affects on our environment and are contributing to the poisoing of our world.

Dno't have a clue about where you live. Likely your browned out grass is a kind that looks great during the summer -- perhaps Bermudagrass? If so, it doesn't remain nicely green during cold weather.

And the grassy clumps in it is a different grass, one adapted to cool weather.

The cold hard facts are that no lawns are composed of only one grass.

My plant zone is 8 in GA. See the grasses

Can't really tell what cool season grass you have there from the picture, but agree that jean001a is correct about the Bermuda. You might be able to stifle and at least reduce the cool season grass by mowing very short, maybe 1-1/2" all season, and not watering. Generally, cool season grasses like to be mowed at a taller height and need much more water than Bermuda. You would gradually be giving the Bermuda an advantage.
If you must use a weed killer like glyphosate on the cool season grass do so in late winter long before the Bermuda thinks about greening up, otherwise if you are too late your lawn will be pock marked until the Bermuda fills back in.
hortster

Good luck with that green grass in your photo. It is poa grass, the most miserable grass there is. I live in western tennessee, Jackson, this grass showed up in my yard 3 years ago. I tried every thing to get rid of it, it is impossible. Over the years it will cover your yard, so I gave up. It will disappear when it gets real hot.

We can't tell you which of three or four warm season grasses your lawn might be composed of. Centipede, St. Augustine, and Bermuda are the most common. Yours looks to be a combination of Centipede and Bermuda.....and Poa annua....the green weed grass.

In my opinion, the best way for homeowners to control Poa is by the careful application of a pre-emergent herbicide in the fall. Such an herbicide is of zero use once the plant is growing. A pre-emergent application, properly timed, can do wonders to control annual weeds (like Poa) .

There's no reason to use Roundup or other post-emergent herbicides. The Poa won't be so obvious when your permanent grass greens up. Just do your research (your local Extension service will be able to help) so that you apply the right chemical, at the right time, and at the right rate. It is NOT impossible to get rid of.