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Solving cubic equations

  1. Mar 30, 2010 #1
    Hi, I've been trying to solve this equation for hours no, hoping somebody here can help.
    I have the equation: -2m2w3 + 15Bmw2 - 27B2 = 0

    where m, B are unknown constants and I'm trying to solve for w. Is there a general formula for solving cubic equations?

    Thanks in advance.
    Last edited: Mar 30, 2010
  2. jcsd
  3. Mar 30, 2010 #2
    Yes, there is. However, it is more complicated than the solution for a quadratic equation. You can look it up in a math handbook, or google it.

    By the way, is your equation cubic? You show only powers [tex]w^2[/tex], but maybe you have a typo.
  4. Mar 30, 2010 #3
    If you are trying to solve for w, all you need to do here is rearrange the terms no?

    -2m2w2 + 15Bmw2 - 27B2 = 0

    Add 27B2 to both sides

    -2m2w2 + 15Bmw2 = 27B2

    factor w2

    w2 ( -2m2 + 15Bm) = 27B2

    Divide by ( -2m2 + 15Bm) --- make sure it is not 0 you need to account for this.

    w2 = 27B2 / (-2m2 + 15Bm)

    Now take the square root of both sides...
  5. Mar 30, 2010 #4


    Staff: Mentor

    Is there a typo somewhere? The topic title suggests you want to know how to solve a cubic equation, but the equation you gave is quadratic in w.
  6. Mar 30, 2010 #5
    Sorry, yes indeed there was a typo, the first term should have been cubed rather than squared.:redface:
  7. Mar 30, 2010 #6
    Yes, I figured that was what is was supposed to be. There is a well know formula and procedure to solve cubic equations.
  8. Mar 30, 2010 #7
    Here are a few pages from my math handbook on cubic solutions.

    Attached Files:

  9. Mar 31, 2010 #8
    Thanks elect_eng.......the scan is quite hard to read but I think I got it......much appreciated.
  10. Mar 31, 2010 #9
    Sorry about the poor resolution. I tried a higher resolution picture and it wouldn't upload. I'll try again tonight just to make sure that you have a good copy. I'll make two separate files - one for each page.
  11. Apr 2, 2010 #10
    Sorry, I took longer than expected to post a better version. I don't know why I had trouble uploading PDFs because my files were smaller than the posted limit. To bypass this trouble, I just rewrote the method and generated my own PDF. This is not a bitmaped PDF, and is hence much smaller in size. It's now all on one page and this makes a nice handy reference sheet.

    Attached Files:

    Last edited: Apr 3, 2010
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