24x^3+24x^2-36x+18=0
Anyone? Thanks!
http://www.wolframalpha.com/input/?i...2-36x%2B18%3D0
we aren't a calculator.
The first thing I would do is divide the equation by 6:
$\displaystyle 4x^2+ 4x^2- 6x+ 3= 0$
Then I would use the "rational root theorem": any rational roots of this equation must be a fraction with numerator a factor of 3 and denominator a factor of 4. That is, the numerator must be one of $\displaystyle \pm 3$, or $\displaystyle \pm 1$ and the denominator must be one of $\displaystyle \pm 4$, $\displaystyle \pm 2$, or $\displaystyle \pm 1$. There are 12 possible combinations. Try each of those. If you find a rational root among those, then you can reduce the equation to a quadratic to find the other roots.
If there is no rational root, then you will just have to use Cardano's formula, which is terribly messy.