\(9+10+11+...+x=1239\)
\(\Leftrightarrow\frac{\left(9+x\right)\left(x-9+1\right)}{2}=1239\)
\(\Leftrightarrow\left(x+9\right)\left(x-8\right)=1239\times2\)
\(\Leftrightarrow x^2+x-72=2478\)
\(\Leftrightarrow\left(x+1\right)x=2478+72\)
\(\Leftrightarrow\left(x+1\right)x=2550=50\cdot51\)
\(\Rightarrow x=50\)