Algebraic equation with radicals

Solve the following equation: $7 x - \frac{3 x ^{2} - 8 x + 1}{x} = (\frac{8}{x} + x)^{2}$ .

~20 minAnswer checked instantlyradical equationsalgebraic manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.a, No. 26

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).