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Topic: Rearranging a cubic equation
Replies: 6   Last Post: Aug 11, 2013 8:31 PM

 Messages: [ Previous | Next ]
 Roland Franzius Posts: 304 Registered: 12/7/04
Re: Rearranging a cubic equation
Posted: Aug 7, 2013 4:42 AM

Am 07.08.2013 08:09, schrieb dwyerdan@gmail.com:
> Hi.
>
> Can anyone re-arrange the following equation to make x the subject of the equation (i.e. x = ...)?
>
> y = (x^3 * a) + (x * b * [x * c + 91]) + (x * d) + (x * e)
>
> It is a real world problem, not a theoretical exercise. I have had a look at the wikipedia page on cubic functions, but I don't understand enough of it to be helpful.
>
> I am struggling to get it into the basic form of a cubic function (f(x) = ax^3 + bx^2 + cx + d).
>
> Any takers?

See

http://www.wolframalpha.com/

The three soltions are

{{x -> -((b c)/(
3 a)) + (2^(
1/3) (273 a b - b^2 c^2 + 3 a d + 3 a e))/(3 a (-819 a b^2 c +
2 b^3 c^3 - 9 a b c d - 9 a b c e -
27 a^2 y + \[Sqrt](4 (273 a b - b^2 c^2 + 3 a d +
3 a e)^3 + (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e - 27 a^2 y)^2))^(1/3)) - (1/(
3 2^(1/3)
a))((-819 a b^2 c + 2 b^3 c^3 - 9 a b c d - 9 a b c e -
27 a^2 y + Sqrt[
4 (273 a b - b^2 c^2 + 3 a d + 3 a e)^3 + (-819 a b^2 c +
2 b^3 c^3 - 9 a b c d - 9 a b c e - 27 a^2 y)^2])^(
1/3))}, {x -> -((b c)/(
3 a)) - ((1 + I Sqrt[3]) (273 a b - b^2 c^2 + 3 a d +
3 a e))/(3 2^(2/3)
a (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d - 9 a b c e -
27 a^2 y + \[Sqrt](4 (273 a b - b^2 c^2 + 3 a d +
3 a e)^3 + (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e - 27 a^2 y)^2))^(1/3)) + (1/(
6 2^(1/3)
a))(1 - I Sqrt[3]) (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e -
27 a^2 y + \[Sqrt](4 (273 a b - b^2 c^2 + 3 a d +
3 a e)^3 + (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e - 27 a^2 y)^2))^(1/3)}, {x -> -((b c)/(
3 a)) - ((1 - I Sqrt[3]) (273 a b - b^2 c^2 + 3 a d +
3 a e))/(3 2^(2/3)
a (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d - 9 a b c e -
27 a^2 y + \[Sqrt](4 (273 a b - b^2 c^2 + 3 a d +
3 a e)^3 + (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e - 27 a^2 y)^2))^(1/3)) + (1/(
6 2^(1/3)
a))(1 + I Sqrt[3]) (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e -
27 a^2 y + \[Sqrt](4 (273 a b - b^2 c^2 + 3 a d +
3 a e)^3 + (-819 a b^2 c + 2 b^3 c^3 - 9 a b c d -
9 a b c e - 27 a^2 y)^2))^(1/3)}}

--

Roland Franzius

Date Subject Author
8/7/13 dwyerdan@gmail.com
8/7/13 William Elliot
8/7/13 Roland Franzius