\begin{tabular}{l} Solve this quadratic equation. \\ \( \qquad 3 x^{2}-4 x=-1 \) \\ \hline\end{tabular}

To solve the quadratic equation \(3x^2 - 4x + 1 = 0\), we can use the quadratic formula \(x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\). Here, \(a = 3\), \(b = -4\), and \(c = 1\). Plugging these values into the formula gives us: 1. Calculate the discriminant: \[ b^2 - 4ac = (-4)^2 - 4 \cdot 3 \cdot 1 = 16 - 12 = 4 \] 2. Use the quadratic formula: \[ x = \frac{{4 \pm \sqrt{4}}}{{2 \cdot 3}} = \frac{{4 \pm 2}}{6} \] 3. This results in two possible solutions: - \(x = \frac{6}{6} = 1\) - \(x = \frac{2}{6} = \frac{1}{3}\) Thus, the solutions to the equation are \(x = 1\) and \(x = \frac{1}{3}\). To make your quadratic experience even better, just remember: factoring, using the quadratic formula, or completing the square are all solid strategies! And don’t forget to double-check your work; it’s way too easy to miss a negative sign or miscalculate!