You forgot to mention the centroid

Geometry Level 4

Let \(m_1, m_2\) and \(m_3\) denote the slopes of the three sides of a triangle \(ABC\), and they satisfy the cubic equation \(y^3 + 8y^2+7y=1 \). Find the slope of the straight line that passes through both the orthocenter and the circumcenter of the triangle \(ABC\).

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