Here is a simpler estimate of N of RSA. Let me know if it helps or is completely wrong. I found it helpful in estimating. However solving the polynomial itself is difficult.

Code:

/*
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/
package rsatest20130621;
/**
*
* @author Trurl
*/
public class Rsatest20130621 {
/**
* @param args the command line arguments
*/
public static void main(String[] args) {
double product = 85, answer;
int x;
//double key;
//System.out.print("Enter the Product of to Prime numbers ");
//product = keyboard.nextDouble();
for (x = 3; x < product; x +=2)
{
//answer = (((Math.pow(product,4)/x) / ((Math.pow(product,4))/((Math.pow(x,4))) + 2 * ((Math.pow(product,2)/x) + Math.pow(product,2)* x) + (Math.pow(x,4)))) - x );
//answer = (( ((Math.pow(product,2)) + (Math.pow(x,3)) ) / product) - product ) ;
answer = ( (((Math.pow(product,2)) / (((Math.pow(product,2)) / x ) + (Math.pow(x,2)))) )) ;
//if ((answer - x) > -1.0 && (answer - x) <= 20.0)
if ((answer - x) > -1.0 && (answer - x) <= 1.0)
{
System.out.println(x);
System.out.println();
System.out.println();
};
}
}
}