Homogeneous radical equation with parameter

Solve the following equation for $x$ : $a^{2} + 2 a x - 3 x^{2} - a^{2} + a x - 6 x^{2} = 2 a^{2} + 3 a x - 9 x^{2}$ .

~15 minAnswer checked instantlyradical equationsparametric equations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.a, No. 30

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