You cannot expect that any of the points at t = -0.5:1/Fs:0.5 is exactly 0.5*max(x). Remember that you evaluate x at some time steps only and rounding errors have to be considered also.
There is an analytical solution also, but you can use fzero to find the searched points. But you have to find the maximum value of the curve at first. Setting the derivative to 0 will help you.