Решить уравнение пожалуста помогите

Решите задачу:

$\frac{(x-2)!}{(x-2-2)!} + \frac{x!}{(x-(x-2))!(x-2)!} =41 \\ \frac{(x-2)!}{(x-4)!} + \frac{x!}{2!(x-2)!} = 41 \\ (x-3)*(x-2) + \frac{x*(x-1)}{2} = 41 \\ \frac{2(x-3)(x-2)+ x^{2} -x}{2} = 41 \\ 2 (x^{2}-5x+6)+ x^{2} -x=82 \\ 2 x^{2} -10x+12+x2-x = 82 \\ 3 x^{2} -11x+12-82 = 0 \\ 3 x^{2} -11x-70 = 0 \\ D = 121+4*3*70 = 121+ 840 = 961 = 31^{2} \\ x_{1} = \frac{11+31}{6} = 7 \\ x_{2} = \frac{11-31}{6} = - \frac{20}{6} = - \frac{10}{3}$