To solve for \( x \) given that the point \( (x, 9) \) lies on the line defined by the equation \( 2y - 10x + 2 = 0 \), we can substitute \( y \) with \( 9 \) in the equation of the line.
Starting with the equation:
\[ 2y - 10x + 2 = 0 \]
Substituting \( y = 9 \):
\[ 2(9) - 10x + 2 = 0 \]
Calculating \( 2(9) \):
\[ 18 - 10x + 2 = 0 \]
Combining the constants:
\[ 20 - 10x = 0 \]
Next, we isolate \( x \):
\[ -10x = -20 \]
Dividing both sides by \(-10\):
\[ x = 2 \]
Thus, the solution for \( x \) is
\[ \boxed{2} \]