There’s no reason to bring the quadratic formula into this. Square roots can be negative, but when talking about the square root it’s normally assumed to be the principal square root, which is the positive one.

I think it’s in the pipeline. AMD has bought Xilinx, which builds FPGAs and already had some AI specific cores in their processors. I believe they’re developing that further and integrating it in their GPUs now.

I haven’t tried with this, but maybe it’s easy to host it locally. That’s what I do with the stable diffusion web UI

Is this tabbed user interface what you’re asking for?
https://books.libreoffice.org/en/IG72/IG7212-UserInterfaceVariants.html#toc8