You can put this solution on YOUR website! If the solutions of a quadratic equation are equal, then its discriminant should be equal to zero.
The given equation is kx^2 - 10x + 5 = 0
Hence, Discriminant D = [(-10)^2 - 4 x k x 5] = 0
=> (100 - 20k) = 0
=> 100 = 20k
=> k 100/20 = 5.
Hence, for k = 5, the solutions of the given quadratic equation are equal.