Answer:
Following are the code to the given question:
#include <iostream>//header file
using namespace std;
int main()//main method
{
   int c= 0;//defining integer variable to count number of solutions
   int x,y,z;//defining integer variable which is used in the loop
   for (x = 0; x <= 100; x++)//defining for loop to x value
      for (y = 0; y <= 100; y++)//defining for loop to y value
         for (z = 0; z <= 100; z++)//defining for loop to z value
            if (4 * x + 3 * y - 9 * z == 5)//use if to check given condition
            {
               c++;//increment count value
               cout << "(" << x << "," << y << "," << z << ")";//print solutions  
               cout << (c % 11? " " : "\n");//use for add file solution in a row
            }
   cout << "\n\nThere are " << c << " solution(s)\n";//print solution couts
   return 0;
}
Output:
Please find the attached file. 
Explanation:
In the above-given code four integer variable "x,y,z, and c" is declared, in which "x,y, and z" is used in the for loop with the if conditional statement that checks the given condition and prints the solution and the "c" variable is used to counts the number of solution, and at the last, it uses the print method to print its values.