Alpertron Number Theory Methods to solve quadratic Diophantine equations by Dario Alejandro Alpern The purpose of this article is to show how to solve the Diophantine Equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. The term Diophantine Equation means that the solutions (x, y) should be integer numbers. For example, the equation 4y2 - 20y + 25 = 0 has solutions given by the horizontal line y = 2.5, but