@Markiyan Hirnyk Thax a lot for your help. I know understood your amazing way. I Just  have two questions.

1. is  0 in above solution global minimum and 479 is global maximim?

2. I tried your code but it is a little different. why is that?

y := (1/2)*((alpha*k^2-3*alpha*k-2*beta)*sqrt(delta^2*(k-1)*(k-2)*(alpha*c-delta)^2)-k*delta*(alpha*k^2-3*alpha*k+2*alpha-2*beta)*(alpha*c-delta))/(delta^2*(alpha*k^2-3*alpha*k-2*beta))

DirectSearch-GlobalOptima(y, {alpha >= 0, beta >= 0, c >= 0, delta >= c*alpha, k >= 0, k <= 1})

DirectSearch+[-0., [-(alpha = 0.115480614666561e-1), -(beta = 0.737582539539197e-2), -(c = .554128006242391), -(delta = 0.639910427648275e-2), -(k = 0.928215339085462e-2)], -486]

Actually i don't want to optimize the inequality. If u<0 has no answer how about u>0?