How Do You Solve for t in a Cubic Parametric Equation?

[jjj888]

Homework Statement

Here's the equation:

slove for t

x=at^3+bt^2+ct+d

Homework Equations

Parametic Equations, removing the t value and such, to "simplify" the equation.

The Attempt at a Solution

This is as far as I got:

(x-d)/t = t^2(a+(b/t)+(c/t^2))

I'm stumped. Is this even possible?

Thanks

 

[spamiam]

There is a general method of expressing the roots of a cubic equation in terms of its coefficients, but it is far more complicated than the quadratic formula. You can find it here: http://en.wikipedia.org/wiki/Cubic_function

Are there any constraints on a, b, c, and d?

 

[jjj888]

Thanks, yea that looks pretty crazy, but interesting. I had a feeling it was headed that way, I wasn't aware of the cubic function. a,b,c,and d are basically a single real number value, if that's what you mean.

Thanks!