Is there a general formula for solving cubic equations?

[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?

Thanks in advance.

 

[elect_eng]

Is there a general formula for solving cubic equations?

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.

 

[Diffy]

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...

 

[Mark44]

Hi, I've been trying to solve this equation for hours no, hoping somebody here can help.
I have the equation: -2m²w² + 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.

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.

 

[dfitz1000]

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

 

[elect_eng]

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

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

 

[elect_eng]

... There is a well know formula and procedure to solve cubic equations.

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

 

[dfitz1000]

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

 

[elect_eng]

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

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.

 

[elect_eng]

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

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.