kinematics equation

This is simply a solution of an algebric quadratic equation, which doesn't involve an physics concept.

Your equaion is:
(1/2).a.t^2 + (vi).t - d = 0
compare with a standard quadratic equation: Ax^2 + Bx + C = 0
it can be seen that
A = a/2
B = (vi)
C = -d
The variable x now becomes the variable t

Since the solution is
x = {-B +/- square-root[ B^2 - 4.A.C]}/2A

you can substtitute the values into the expression and find out the solution yourself.