repaint() or update(Graphics g)

I went through the time consuming process of completing my paint method. I did not know how to call the paint method. I tried with no arguments but it required them. I tried to create an update method to just call the repaint method. It still did not work. I finally tried to call the QuadraticSolver method in the Applet class. It worked and now my applet combined with my other methods was working. However, I still have my other components to complete such as the Javadoc.