How did scientists discover chemotherapy and radiation to heal cancer patients?

It really comes from quantum physics. Basically bombarding small particals against others. Hence the term partical physics. We get the same result,although to a much lesser extent with X-Rays, MRI’S or even CT’S(which is a fancier x-ray). With chemo, unstable nucleotides are used, which give off particles which essentially blast the tumor cell, and kill it. Remember a cancer,or a tumor, is a cell which does not know it’s own boundry’s, thus each cell just keeps on growing on top of each other cell and thus may or may not spread …growing over completely different cells,thus inhibiting them.
Chemo is an atomic form of radiation. And again, it is based primarily on partical physics. Using unstable atoms energy to disrupt the growth of other cells. Thats as simple as I can make it.

it has been long known that exposure to radiation will damage and eventually kill tussie.
It’s not much of a stretch to figure out that small doses of targeted radiation will whatever tissue is exposed to it.
Chemotherapy was developed by testing millions of chemicals in the lab to see what effect they had on cancerous tissue and healthy tissue and organs.
When a chemical is found that kills cancer but not healthy tissue, it is adapted for use in chemo.

"Marie klodowska Curie discovered the mysterious element radium. It opened the door to deep changes in the way scientists think about matter and energy. She also led the way to a new era for medical knowledge and the treatment of diseases." —
I read her story a while ago – fascinating since we now know so much more, but educate yourself on Madam Curie