# Solving cubic equations

1. Mar 30, 2010

### dfitz1000

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?

Last edited: Mar 30, 2010
2. Mar 30, 2010

### elect_eng

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 $$w^2$$, but maybe you have a typo.

3. Mar 30, 2010

### Diffy

If you are trying to solve for w, all you need to do here is rearrange the terms no?

-2m2w2 + 15Bmw2 - 27B2 = 0

-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...

4. Mar 30, 2010

### 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.

5. Mar 30, 2010

### dfitz1000

Sorry, yes indeed there was a typo, the first term should have been cubed rather than squared.

6. Mar 30, 2010

### elect_eng

Yes, I figured that was what is was supposed to be. There is a well know formula and procedure to solve cubic equations.

7. Mar 30, 2010

### elect_eng

Here are a few pages from my math handbook on cubic solutions.

#### Attached Files:

• ###### CubicSolution.pdf
File size:
83.8 KB
Views:
205
8. Mar 31, 2010

### dfitz1000

Thanks elect_eng.......the scan is quite hard to read but I think I got it......much appreciated.

9. Mar 31, 2010

### elect_eng

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.

10. Apr 2, 2010

### elect_eng

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:

• ###### CubicSolution.pdf
File size:
21.3 KB
Views:
90
Last edited: Apr 3, 2010