using System;
using System.Linq;

public class Test
{
	public static void Main()
	{
		var s = "background-image: url('https://s...content-available-to-author-only...s.com/files.domain.com/uploads/image/file/168726/carousel_IMG_6455.jpg')";
		var res = s.Split(new[] {"'"}, StringSplitOptions.None).Where(v => v.StartsWith("http")).FirstOrDefault();
		Console.WriteLine(res);
	}
}