Is there a such thing as a DX to FX nikon converter?

I have 2 separate cameras and bought a DX lens for a great deal but I wish I could use it on my d750 without losing the quality.

No. You can use DX lenses on FX bodies directly because both have the same F mount. When you do use the DX lens, the FX body will need to be put into a crop mode. It may do this automatically. If you were to take a shot with the FX body NOT in DX mode, the resulting image would have black edges because the sensor is larger than the image circle being emitted from the rear of all DX lenses.

It's only with Canon where you can't put lenses that are specifically designed for APS-C cameras onto full-frame cameras. They simply will not mount nor is there a converter to do so.

For all brands, you can put a lens designed for a larger format onto a camera of a smaller format (e.g. FX lens on DX body) without any issues. Canon is the same way. You can put a full-frame Canon lens onto any camera APS-C camera without the need of any adapters.

What is there to convert? The mount is the same. What loss of quality? There's no such thing. That is if you are able to take a shot with the DX lens on the FX camera without damaging the camera's reflex mirror. That's issue here. It's physical. DX lenses have a protruding rear end designed to focus on smaller sensors. That in turn gets in the way of the FX camera's reflex mirror as it swings up when taking a photo.

Even if you are able to use the DX lens, it won't cover the entire full-frame sensor because it projects an image that's smaller. The result would be a photo (same quality) that is small (cropped) with ugly large dark borders around it.

The rule is simple. When using FX cameras, use only FX lenses. If that second camera is DX then you surely have no problem at all using your DX lenses with it. You're just being importunate.

All FX bodies will mount and shoot DX lenses. You would need to use crop mode to avoid strong vignetting. There's no chance of damaging the mirror!

I really do not know why you are concerned about "quality" of DX cameras

Here are two shots that were taken with an old Nikon D100, DX with a 6-mp sensor. It was good enough to be published in two different magazines The links are to reduced resolution image files (600 x 400 @ 72 ppi) for posting on the Internet.

The third photo was shot using a newer Nikon D500, DX with a 20 mp sensor, again resized for publishing on the Internet.

As mentioned before, you need NO converter to use a DX lens on an FX camera, nor an FX lens on a DX camera.

Just make sure that your exposures are dead on and that you use the lowest ISO setting on the camera that will allow a short enough shutter speed to stop any action.