[tex]C^2_x +xA^1_x =22 \Leftrightarrow \dfrac{x!}{2!(x-2)!} + x\cdot x =22 \Leftrightarrow
\\\;\\
\Leftrightarrow \dfrac{(x-2)!\cdot (x-1)x}{2(x-2)!} +x^2 -22 =0 \Leftrightarrow \dfrac{x^2-x}{2} +x^2-22=0 \Leftrightarrow
\\\;\\
\Leftrightarrow x^2-x+2x^2-44 = 0 \Leftrightarrow 3x^2-x-44 = 0
\\\;\\ \it{Solutia\ naturala\ a\ ecuatiei\ este\ x = 4}.[/tex]
