# Math Help - Can anyone solve this cubic for me?

1. ## Can anyone solve this cubic for me?

24x^3+24x^2-36x+18=0

Anyone? Thanks!

2. Originally Posted by BigMath
24x^3+24x^2-36x+18=0

Anyone? Thanks!
The first thing I would do is divide the equation by 6:
$4x^2+ 4x^2- 6x+ 3= 0$

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 $\pm 3$, or $\pm 1$ and the denominator must be one of $\pm 4$, $\pm 2$, or $\pm 1$. 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.