Let x-1 = t and t^2 = a, which is positive. Then, the equation reduces to 7a^3 +100a^2 +80a=0 > a=0 or 7a^2+100a+80=0. The latter has no positive roots. So, a=0 > x=1.
Slightly disappointed with the approach of interpretation (explanation). Lack of straightforwardness and lack of clarity. Lazy approach! I seek forgiveness for harsh comment!