Use the quadratic formula to solve for \( x \). \[ 6 x^{2}-2 x-1=0 \] (If there is more than one solution, separate them with commas.) \( x=\square \)

Solve the equation \( 6x^{2}-2x-1=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(6x^{2}-2x-1=0\) - step1: Solve using the quadratic formula: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 6\left(-1\right)}}{2\times 6}\) - step2: Simplify the expression: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 6\left(-1\right)}}{12}\) - step3: Simplify the expression: \(x=\frac{2\pm \sqrt{28}}{12}\) - step4: Simplify the expression: \(x=\frac{2\pm 2\sqrt{7}}{12}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{2+2\sqrt{7}}{12}\\&x=\frac{2-2\sqrt{7}}{12}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{7}}{6}\\&x=\frac{2-2\sqrt{7}}{12}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{7}}{6}\\&x=\frac{1-\sqrt{7}}{6}\end{align}\) - step8: Rewrite: \(x_{1}=\frac{1-\sqrt{7}}{6},x_{2}=\frac{1+\sqrt{7}}{6}\) The solutions to the quadratic equation \(6x^{2}-2x-1=0\) using the quadratic formula are \(x_{1}=\frac{1-\sqrt{7}}{6}\) and \(x_{2}=\frac{1+\sqrt{7}}{6}\).