**Solution:**

Let the number of wickets taken by Zahir be x.

=> Number of wickets taken by Harbhajan = 2x - 3.

According to the given condition,

x(2x – 3) = 20

=> 2x^{2} – 3x = 20

=> 2x^{2} – 3x – 20 = 0

**Therefore, the required quadratic equation is 2x**^{2} – 3x – 20 = 0.