Ready solution of the problem. The sorcerer of Arutyunov. Task number 82.

81 - 90. Using the theory of quadratic forms, we can reduce the line equation of the second order to the canonical form.

82. 5x2 + 2√3xy + 3y2 = 12

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)