Downsizing image without losing quality

[t2x]

I have tried many things and I am tearing my hear out as I write this one-handed. I have a logo that is 709 by 413 and I want to resize it to 86 by 50. I have tried using Image => Image Size => Bicubic Sharper but I still get these horrible results on my webpage (using Wordpress if that helps). I have attached a before and after photo.

Before:

Settings:

After:

In Photoshop

It looks really bad particularly on my mobile site. This makes me very sad. I would appreciate any help!

[Nancy OShea]

If this were my project, I would recreate the logo and text in Illustrator as a vector graphic and export to SVG.  You'll get much nicer results because SVG does not degrade when rescaled up or down.   At such a small size, raster images will look terribly pixelated especially on High DPI screens.  There's nothing much you can do about that.