We designed and implemented quadratic formula, cubic formula, and quartic formula solvers using the formulas in the Wikipedia articles:
https://en.wikipedia.org/wiki/Quadratic_formula
https://en.wikipedia.org/wiki/Cubic_function
https://en.wikipedia.org/wiki/Quartic_function
We tested our C# implementation against:
https://keisan.casio.com/exec/system/1181809415
http://www.wolframalpha.com/widgets/view.jsp?id=3f4366aeb9c157cf9a30c90693eafc55
https://keisan.casio.com/exec/system/1181809416
Here are screenshots of the C# application:
C# source code files for the application:
Numerical Explorations 