3x^2-2ax+2a-3>0
3(x^2-1)-2a(x-1)>0
3(x+1)(x-1)-2a(x-1)>0
(x-1)(3x+3-2a)>0
(x-1)[x-(2a-3)/3]>0
若(2a-3)/33
则x>(2a-3)/3,x0
则x不等于1