This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, b, c [is a member of] R, the set of real numbers, are presented. Case II deals with the geometrical solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when b [is a member of] R, the set of real numbers; and a, c [is a member of] C, the set of complex numbers. Finally, the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, c [is a member of] R, the set of real numbers, and b [is a member of] C, the set of complex numbers, are presented in case III. (Contains 3 figures.)