If x is real, then the value of x2+34x-71x2+2x-7 does not lie between

Let y=x2+34x-71x2+2x-7⇒x2(y-1)+2(y-17)x+(71-7y)=0For real values of x, its discriminant D⩾0⇒4(y-17)2-4(y-1)(71-7y)⩾0⇒(y2-3+y+289)-(71y-7y2-71+7y)⩾0⇒y2-14y+45⩾0⇒(y-5)(y-9)⩾0It is possible when both y-5 and y-9 are negative or both positive. Let y-5≤0⇒y≤5 and y-9⩽0⇒y≤9.Hence y≤5    ...(i)If y-5≥0⇒y⩾5 and y-9≥0⇒y≥9.Hence y≥9.Therefore y does not lie between 5 and 9.