To get a charge -1$e$ particle from the up (u) and down (d) quarks you need three d quarks each of chargehaving charge -1/3 $e$. This means that flavour part of the wavefunction is symmetric in the three quarks. The color part is necessarily antisymmetric so as to get the colour singlet required by confinement. As Fermi statistics requires the combined state be antisymmetric, the spin part of the state would have to be symmetric and so the total spin will be j=3/2. The resulting particle cannot be a spin 1/2 hadron, and is instead the spin 3/2 $\Delta^-$.
Similarly three u quarks gives the $\Delta^{++}$