My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <iomanip>
       
#include <cmath>
       
 
       
//#define SLOW

       
 
       
// compute s(r) according to problem statement

       
double s(double r)
       
{
       
  double result = 0;
       
  double x = 1; // r^0 is always 0
       
  for (int k = 1; k <= 5000; k++)
       
  {
       
#ifdef SLOW
       
    result += (900 - 3 * k) * pow(r, k - 1);
       
#else
       
    result += (900 - 3 * k) * x;
       
    x *= r;
       
#endif
       
  }
       
  return result;
       
}
       
 
       
int main()
       
{
       
  // initial lower and upper bounds
       
  double lower = 0;
       
  double upper = 2;
       
 
       
  // until the range is small enough
       
  while (upper - lower > 0.0000000000001)
       
  {
       
    double mid = (upper + lower) / 2;
       
    // find result at midpoint
       
    double current = s(mid);
       
 
       
    // adjust borders
       
    if (current < -600000000000.0)
       
      upper = mid;
       
    else
       
      lower = mid;
       
  }
       
 
       
  // print result (use midpoint but upper and/or lower should yield the same output)
       
  std::cout << std::fixed << std::setprecision(12) << (upper + lower) / 2 << std::endl;
       
  return 0;
       
}

This solution contains 6 empty lines, 7 comments and 6 preprocessor commands.