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.
\(9+\frac{27}{x}+\frac{8}{x^2} = \frac{7}{x^2} + \frac{24}{x} + 5\)
Multiply both sides by x2,
\(\Rightarrow 9x^2 + 27x + 8 = 7 + 24x + 5x^2\)
\(\Rightarrow 4x^2 + 3x +1 =0\)
\(=\frac{- 3\pm \sqrt{9-16}}{8} = \frac{-3 \pm \sqrt{7}i}{8}\)
\(=\boxed{ \frac{-3 + \sqrt{7}i}{8} , \frac{-3-\sqrt{7}i}{8}}\)