Equation of the plane making a, b & c intercepts with X, Y & Z axes respectively is

But, the plane makes equal intercepts on the co-ordinate axes

Therefore, a = b = c

Therefore the equation of the plane is

x + y + z = a

As plane passes through the point (2, -3, 7),

Substituting x = 2, y = -3 & z = 7

2 – 3 + 7 = a

Therefore, a = 6

Hence, required equation of plane is

x + y + z = 6