proving limit for given values of epsilon

For the limit

lim_x->1 (4 + x - 3x^3) = 2

I'm trying to find values of delta that
correspond to the epsilon values
1 and .1

I start off by finding a corresponding
delta for epsilon = 1
and expressing it this way:

|(4 + x - 3x^3) - 2| < 1
whenever
0 < |x - 1| < delta

Now I can approach the solution
to this problem by first making an
educated guess for what delta
would be. In this case,
I can started by factoring
2 + x - 3x^3

This is where I am stuck though.
This part seems convoluted.
I know one factor of this polynomial
is (x - 1) and the other two are imaginary
factors (3 +/- sqrt(9 - 24))/-6

Am I going about this all wrong?

--
conrad
.

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