Ive the quadratic equation. \( -9 x^{2}-2 x+3=0 \) Vrite one exact solution in each box. You can add or remove boxes. If there are no olutions, remove all boxes.

Solve the equation \( -9x^2-2x+3=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(-9x^{2}-2x+3=0\) - step1: Multiply both sides: \(9x^{2}+2x-3=0\) - step2: Solve using the quadratic formula: \(x=\frac{-2\pm \sqrt{2^{2}-4\times 9\left(-3\right)}}{2\times 9}\) - step3: Simplify the expression: \(x=\frac{-2\pm \sqrt{2^{2}-4\times 9\left(-3\right)}}{18}\) - step4: Simplify the expression: \(x=\frac{-2\pm \sqrt{112}}{18}\) - step5: Simplify the expression: \(x=\frac{-2\pm 4\sqrt{7}}{18}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{-2+4\sqrt{7}}{18}\\&x=\frac{-2-4\sqrt{7}}{18}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{-1+2\sqrt{7}}{9}\\&x=\frac{-2-4\sqrt{7}}{18}\end{align}\) - step8: Simplify the expression: \(\begin{align}&x=\frac{-1+2\sqrt{7}}{9}\\&x=-\frac{1+2\sqrt{7}}{9}\end{align}\) - step9: Rewrite: \(x_{1}=-\frac{1+2\sqrt{7}}{9},x_{2}=\frac{-1+2\sqrt{7}}{9}\) The solutions to the quadratic equation \( -9x^{2}-2x+3=0 \) are: \( x_{1}=-\frac{1+2\sqrt{7}}{9} \) \( x_{2}=\frac{-1+2\sqrt{7}}{9} \)