From 2a2+a(n-5)=0.

2C(n，2)-C(n，5)=0

2C(n，2)=C(n，5)

That is, 2n (n- 1)/2 = n (n-1) (n-2) (n-3) (n-4)/120, n, n-1is not equal to zero, so it is obtained that

(n-2)(n-3)(n-4)= 120 = 2 * 3 * 4 * 5 = 4 * 5 * 6

n=8