Given the equations:

Line: \(2y = x + 5\)

Curve: \(y = x^2 - 4x + 7\)

Substitute \(y\) from the line equation into the curve equation:

\(y = \frac{x + 5}{2}\)

Substitute into the curve equation:

\(\frac{x + 5}{2} = x^2 - 4x + 7\)

Multiply through by 2 to eliminate the fraction:

\(x + 5 = 2x^2 - 8x + 14\)

Rearrange to form a quadratic equation:

\(2x^2 - 9x + 9 = 0\)

Factor or use the quadratic formula to solve for \(x\):

\(x = 3\) or \(x = \frac{1}{2}\)