Range for an Inequality

Find the greatest integer value of $x$ in order that $7 x^{2} + 11$ may be greater than $x^{3} + 17 x$ .

~10 minAnswer checked instantlyInequalitiesCubic polynomials

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 14

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