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# Algebra

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Find all values of x such that    9 + 27/x + 8/x^2 = 7/x^2 + 24/x + 5
If you find more than one value, then list your solutions, separated by commas.

Jul 18, 2022

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$$9+\frac{27}{x}+\frac{8}{x^2} = \frac{7}{x^2} + \frac{24}{x} + 5$$

Multiply both sides by x2,

$$\Rightarrow 9x^2 + 27x + 8 = 7 + 24x + 5x^2$$

$$\Rightarrow 4x^2 + 3x +1 =0$$

$$=\frac{- 3\pm \sqrt{9-16}}{8} = \frac{-3 \pm \sqrt{7}i}{8}$$

$$=\boxed{ \frac{-3 + \sqrt{7}i}{8} , \frac{-3-\sqrt{7}i}{8}}$$

Jul 18, 2022