In this study, a special standard quadratic congruence of composite modulus-an even multiple of Power of an odd positive integer is studied rigorously and a very simple formula for the solutions of the congruence is established. It is found that congruence has many incongruent solutions. The solutions can be obtained without any pen & Paper. It can be calculated orally. The congruence was not formulated earlier. This is the first time a formulation of the solutions of the said congruence is made available by the author. This is the merit of the paper.