sqrt(7+6x+x^2)=ax-8a+4
sqrt(7+6x+x^2)=a(x-8)+4
7+6x+x^2=a^2(x-8)^+8a(x-8)+16
7+6x+x^2=a^2(x^2-16x+64)+8ax-64a+16
7+6x+x^2=a^2x^2-16a^2x+64a^2+8ax-64a+16
(a^2-1)x^2+(8a-16a^2+6)x+(64a^2-64a+16+7)=0
(a^2-1)x^2+(8a-16a^2+6)x+(8a-4)^2-7=0
(a^2-1)x^2-(16a^2-8a+1)x+(8a-4)^2=0
(a^2-1)x^2-(4a-1)^2 x+(8a-4)^2=0
(4a-1)^4-4(a^1-1)(8a-4)^2=0
288a^2-272a+65=0
a=17/36-1/36 i sqrt(7/2)
a=17/36+1/36 i sqrt(7/2)