[tex]\left(\dfrac{x^2+6}{x}\right)^2 = 25\\ \Leftrightarrow \, \left(\dfrac{x^2+6}{x}\right)^2 = 5^2 \,\Leftrightarrow \, \left(\dfrac{x^2+6}{x}\right)^2 = 5^2\\ \\\Leftrightarrow \, \dfrac{x^2+6}{x} = \pm 5 \,\Leftrightarrow \, x^2+6 = \pm 5x\\ \\ \Leftrightarrow \, x^2\mp 5x +6 = 0\\ \\ \Delta = (\mp 5)^2 - 4\cdot 1\cdot 6 = 25-24 = 1[/tex]
[tex]\Rightarrow\,x_{1,2} = \dfrac{\pm 5 \pm \sqrt{1}}{2}\Rightarrow\, S = \left\{\dfrac{-5-1}{2};\,\dfrac{-5+1}{2};\,\dfrac{5-1}{2};\,\dfrac{5+1}{2}\right\}\\ \\ \Rightarrow \,\boxed{\boxed{S = \left\{-3;\,-2;\,2;\,3\right\}}}[/tex]
