[tex]x - \frac{864}{x} = 12 \sqrt{3} [/tex]
[tex]x - \frac{864}{x} - 12 \sqrt{3} = 0[/tex]
[tex] \frac{ {x}^{2} - 864 - 12 \sqrt{3} x }{x} = 0[/tex]
[tex] {x}^{2} - 864 - 12 \sqrt{3} x = 0[/tex]
[tex] {x}^{2} - 12 \sqrt{3} - 864 = 0[/tex]
[tex]x = \frac{ - ( - 12) \times \sqrt{3} + \sqrt{ {( - 12 \sqrt{3)} }^{2} - 4 \times 1 \times ( - 864) } }{2 \times 1} [/tex]
[tex]x = \frac{12 \sqrt{3} + \sqrt{144 \times 3 + 3456} }{2} [/tex]
[tex]x = \frac{12 \sqrt{3} + \sqrt{3888} }{2} [/tex]
[tex]x = \frac{12 \sqrt{3} + 36 \sqrt{3} }{2} [/tex]
[tex]x = \frac{12 \sqrt{3} - 36 \sqrt{3} }{2} [/tex]
[tex]x = 24 \sqrt{3} \\ x = - 12 \sqrt{3} [/tex]
