4x²-4x＞15.===>4x²-4x+1＞16.===>(2x-1)²＞16.===>|2x-1|＞4.===>2x-1＞4,或2x-1＜-4,===>x＞5/2,或x＜-3/2.∴x∈(-∞,-3/2)∪(5/2,+∞).