Number of real solution(s) of the equation |x−3|3x2−10x+3=1 is

Case (i) Let 3x2−10x+3=0⇒ (3x−1)(x−3)=0⇒ x=13 or x=3 But for x=3 , base |x−3|=0 , which does not satisfy the equation. Case (ii) |x−3|=1⇒ x=2 or x=5 Hence, three solutions x=13,2,5