To solve the equations given, we first need to expand the expressions that are squared:

1) (х-7)^2 = (9-x)^2
х^2 - 14х + 49 = 81 - 18x + x^2
Subtract х^2 from both sides:
-14х + 49 = 81 - 18x + x^2 - х^2
Rearrange the terms:
-14x + 49 = 81 - 18x + 49
Combine like terms:
-14x = 81 - 18x
4x = 32
x = 8

2) (х+9)^2 = (10-x)^2
x^2 + 18x + 81 = 100 - 20x + x^2
Subtract x^2 from both sides:
18x + 81 = 100 - 20x + x^2 - x^2
Rearrange the terms:
18x + 81 = 100 - 20x
Combine like terms:
38x = 19
x = 19/38

Therefore, the solutions to the given equations are:
x = 8 , x = 19/38