According to the question we have

**A(2,−5) and B(−2,9)**

Let the points be P(x,0).

So, AP=PB and AP^{2}=PB^{2}

⇒(x−2)^{2}+(0+5^{)2 }= (x+2)^{2}+(0−9)^{2}

⇒x^{2}+4−4x+25=x^{2}+4+4x+81

⇒x^{2}+29−4x=x^{2}+85+4x

⇒−4x−4x=85−29

⇒−8x=56

⇒x=−7

**Hence, point on the x-axis which is equidistant from (2,−5) and (−2,9) is (−7,0).**