To simplify the expression \( 18x^2 - 12x + 63x \), you first combine like terms. The terms \( -12x \) and \( +63x \) are like terms.
So, we combine them:
\[ -12x + 63x = 51x \]
Now, substitute back into the expression:
\[ 18x^2 + 51x \]
Thus, the simplified form of the expression \( 18x^2 - 12x + 63x \) is:
\[ \boxed{18x^2 + 51x} \]