Solve the inequality. Write the solution set in interval notation if possible. Simplify your answer, if necessary. \[ 8-9 x>4 x^{2} \] The solution set is \( \square \). (ロ, \( \square \) [ \( [\square, \square][\square, \square) \)

Solve the equation \( 8-9x>4x^{2} \). Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: \(8-9x>4x^{2}\) - step1: Move the expression to the left side: \(8-9x-4x^{2}>0\) - step2: Rewrite the expression: \(8-9x-4x^{2}=0\) - step3: Add or subtract both sides: \(-9x-4x^{2}=-8\) - step4: Divide both sides: \(\frac{-9x-4x^{2}}{-4}=\frac{-8}{-4}\) - step5: Evaluate: \(\frac{9}{4}x+x^{2}=2\) - step6: Add the same value to both sides: \(\frac{9}{4}x+x^{2}+\frac{81}{64}=2+\frac{81}{64}\) - step7: Simplify the expression: \(\left(x+\frac{9}{8}\right)^{2}=\frac{209}{64}\) - step8: Simplify the expression: \(x+\frac{9}{8}=\pm \sqrt{\frac{209}{64}}\) - step9: Simplify the expression: \(x+\frac{9}{8}=\pm \frac{\sqrt{209}}{8}\) - step10: Separate into possible cases: \(\begin{align}&x+\frac{9}{8}=\frac{\sqrt{209}}{8}\\&x+\frac{9}{8}=-\frac{\sqrt{209}}{8}\end{align}\) - step11: Solve the equation: \(\begin{align}&x=\frac{\sqrt{209}-9}{8}\\&x=-\frac{\sqrt{209}+9}{8}\end{align}\) - step12: Determine the test intervals: \(\begin{align}&x<-\frac{\sqrt{209}+9}{8}\\&-\frac{\sqrt{209}+9}{8}\frac{\sqrt{209}-9}{8}\end{align}\) - step13: Choose a value: \(\begin{align}&x_{1}=-4\\&x_{2}=-1\\&x_{3}=2\end{align}\) - step14: Test the chosen value: \(\begin{align}&x<-\frac{\sqrt{209}+9}{8}\textrm{ }\textrm{is not a solution}\\&-\frac{\sqrt{209}+9}{8}\frac{\sqrt{209}-9}{8}\textrm{ }\textrm{is not a solution}\end{align}\) - step15: The final solution is \(-\frac{\sqrt{209}+9}{8}4x^{2}\) is \(-\frac{\sqrt{209}+9}{8}