There is also a good blog post about same subject: http://playtechs.blogspot.kr/2007/04/aiming-at-moving-target.html. It also contains more complex samples that include gravity.

The author has done more simplification, which results in more compact code:

double time_of_impact(double px, double py, double vx, double vy, double s)
{
    double a = s * s - (vx * vx + vy * vy);
    double b = px * vx + py * vy;
    double c = px * px + py * py;

    double d = b*b + a*c;

    double t = 0;
    if (d >= 0)
    {
        t = (b + sqrt(d)) / a;
        if (t < 0)
            t = 0;
    }

    return t;
}

There is also a good blog post about same subject: http://playtechs.blogspot.kr/2007/04/aiming-at-moving-target.html. It also contains more complex samples that include gravity.

The author has done more simplification, which results in more compact code:

double time_of_impact(double px, double py, double vx, double vy, double s)
{
    double a = s * s - (vx * vx + vy * vy);
    double b = px * vx + py * vy;
    double c = px * px + py * py;

    double d = b*b + a*c;

    double t = 0;
    if (d >= 0)
    {
        t = (b - sqrt(d)) / a;
        if (t < 0) 
        {
            t = (b + sqrt(d)) / a;
            if (t < 0)
                t = 0;
        }
    }

    return t;
}

Update: Original author took into account only bigger root. But in case of smaller root being non-negative, it results in better solution, since time of impact is smaller. I have updated the code correspondingly.