Given that $x = \frac{5}{7}$ is a solution to the equation $56 x^2 + 27 = 89x - 8,$ what is the other value of $x$ that will solve the equation? Express your answer as a common fraction.
56x2 + 27 = 89x - 8
56x2 - 89x + 35 = 0
Since x = 5/7 is a solution; one factor will be 7x - 5: the other factor will be 8x - 7:
(7x - 5)(8x - 7) = 0
Either 7x - 5 = 0 or 8x - 7 = 0
7x = 5 8x = 7
x = 5/7 x = 7/8