Let the point be P(x, y). Since it lies on the x-axis
∴ y = 0 i.e., required point be (x, 0). Since the required point is equidistant from points A(7, 6) and B(3, 4) ⇒ PA = PB
⇒ √(x−7)2+(0−6)2 = √(x−3)2+(0−4)2
⇒ √x2+49−14x+36 = √x2+9−6x+16
⇒ x2 - 14x + 85 = x2 - 6x + 25 ⇒ - 14x + 6x = 25 - 85 ⇒ 8x = 60
⇒ x =

15

2

∴ The required point is (

15

2

,0)