using System;

using System.Text.RegularExpressions;

​

public class Program

{

    public static void Main()

    {

        //Console.WriteLine("Hello World");

        var image = "background-image: url('https://s3-eu-west-1.amazonaws.com/files.domain.com/uploads/image/file/168726/carousel_IMG_6455.jpg')";

        image = image.Replace(@"'", "\"");

        //  Console.WriteLine(image);

        Match match = Regex.Match(image, @"([""'])(?:(?=(\\?))\2.)*?\1");

        if (match.Success)

        {

            Console.WriteLine(match.Value);

        }

    }

}