|x+3|-|x-1|≤a^2-3a
→|x+3|-|x-1|≤|(x+3)+(1-x)|≤a^2-3a
→a^2-3a-4≥0
→(a+1)(a-4)≥0
→a≤-1,a≥4
故实数a取值范围为{a|a≤-1}∪{a|a≥4}