Solve the quadratic formula to solve \( 9 x^{2}=-12 x+2 \). \[ x=\square \]

Solve the equation \( 9x^2=-12x+2 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(9x^{2}=-12x+2\) - step1: Move the expression to the left side: \(9x^{2}+12x-2=0\) - step2: Solve using the quadratic formula: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 9\left(-2\right)}}{2\times 9}\) - step3: Simplify the expression: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 9\left(-2\right)}}{18}\) - step4: Simplify the expression: \(x=\frac{-12\pm \sqrt{216}}{18}\) - step5: Simplify the expression: \(x=\frac{-12\pm 6\sqrt{6}}{18}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{-12+6\sqrt{6}}{18}\\&x=\frac{-12-6\sqrt{6}}{18}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{-2+\sqrt{6}}{3}\\&x=\frac{-12-6\sqrt{6}}{18}\end{align}\) - step8: Simplify the expression: \(\begin{align}&x=\frac{-2+\sqrt{6}}{3}\\&x=-\frac{2+\sqrt{6}}{3}\end{align}\) - step9: Rewrite: \(x_{1}=-\frac{2+\sqrt{6}}{3},x_{2}=\frac{-2+\sqrt{6}}{3}\) The solutions to the quadratic equation \(9x^{2}=-12x+2\) are \(x_{1}=-\frac{2+\sqrt{6}}{3}\) and \(x_{2}=\frac{-2+\sqrt{6}}{3}\).