I hope you aren’t wasting a lot of time solving quadratic equations by hand. You’ve done it before, you can do it again, but it’s something you can just as easily tell a computer to do for you.
A quick google search gives you lots of options for entering coefficients and popping out the answer. Some of you may be familiar with Mathematica or Matlab and so can turn to those languages.
If you have a TI89 calculator, you’re in luck, as finding polynomial zeros are already programmed in for you (or you can use the solve function). See me if you need a tip.
If you have a TI83, you just need to take a few minutes to build your own program: http://www.tc3.edu/instruct/sbrown/ti83/quadrat.htm#Enter
If you don’t at least have the equivalent of a TI83 graphing calculator, see me. You need a good portable number cruncher that can make plots for you.