M.A. Gopalan, V. Sangeetha, Manju Somanath, Observations on the Ternary Quadratic Equation X2=24α2+Y2, BSMaSS Volume 10, The Bulletin of Society for Mathematical Services and Standards (Volume 10) https://www.scipress.com/BSMaSS.10.59 Abstract: The Ternary Quadratic Equation X<sup>2</sup>=24α<sup>2</sup>+Y<sup>2 </sup>is Considered.Employing its Non-Zero Integral Solutions, Relations among a few Special Polygonal Numbers are Determined. Keywords: Integral Solutions, Polygonal Numbers, Ternary Quadratic