If $(\mathrm{\alpha },\mathrm{\beta })$ is the orthocenter of the triangle ABC with vertices
A(3, -7), B(-1, 2) and C(4, 5) then $9\mathrm{\alpha }-6\mathrm{\beta }+60$ is equal to

Altitude AD 5x + 3y + 6 = 0,
 Altitude BE 4x - 9y + 29 = 0
solve the above equations, we get
 $$\begin{gathered} Orthocenter (\mathrm{\alpha },\mathrm{\beta })=\left(\frac{-141}{57},\frac{121}{57}\right) \\ now 9\mathrm{\alpha }-6\mathrm{\beta }+60=25 \end{gathered}$$