Since the point is on x-axis, therefore coordinate of y-axis is zero.
Therefore the point is P(k, 0) which is equidistance from A(5, 9) and B(- 4, 6)
PA = PB
\(\sqrt{(5 - k)^2 + 9^2}\) = \(\sqrt{(-4 - k)^2 + 6^2}\)
On squaring both sides
(5 - k)2 + 92 = (- 4 - k)2 + 62
25 - 10k + k2 + 81 = 16 - 8k + k2 + 36
25 - 2k + 81 = 16 + 36 - 25 - 81
k = 27
Therefore coordinate is (27, 0)