The line \(y=3x+4\) meets the curve \(y=2x^2+8x+1\) at two points \(A\) and \(B\).
Find the equation of the perpendicular bisector of \(AB\), giving your answer in the form \(ax+by+c=0\), where \(a,b\) and \(c\) are integers.[9]
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