Resize image pix without loosing quality

When you go from 1400 pixels wide to 750 pixels wide, you throw out half the information, so in that sense there is obviously a quality loss.

But more to the point, resampling always softens an image. Sharp edges turn slightly fuzzy, that's inevitable. Standard procedure is therefore to carefully sharpen after resampling. It doesn't necessarily take much, just enough to rebuild the edges and transitions.

Photoshop's resampling algorithms have some sharpening built in. "Bicubic" has a little, "Bicubic smoother" very little, and "Bicubic sharper" quite a lot. But for best results you should do it manually and visually at 100% view.

Which brings up another point. Resampling also happens to the on-screen display, when you view at any other zoom ratio than 100%. So to critically evaluate sharpness, you must view at 100%. This maps one image pixel to exactly one screen pixel, and is the only entirely accurate view.

When you change the aspect ratio of an image you have basically three choices: crop part of the image, stretch the image or have letterboxing.

If you reduce the image size it shouldn't normally reduce the quality.