I purchased eggs from the refrigerator in a local grocery store...When arriving home I missed and left them on the floor in my house in the plastic grocery bag still in the carton for 2 weeks! The temperature in my house stays on 76-78 degrees here in Florida.  Is there a test that I can do here at home to see if the eggs have spoiled or have salmonella, or should I just throw them away? When I found them here I put them in my refrigerator but have not used them. 
Aquafaba! (also known as chickpea water) Here's a good recipe from Serious Eats:  https://www.seriouseats.com/recipes/2016/03/easy-vegan-mayo-aquafaba-recipe-vegan-experience.html 