The movement of the progress bar may be uneven because questions can be worth mo Solve for \( x \) : \( 6 x^{2}-13 x+5=0 \) \( x x=-\frac{1}{3} \) or \( x=-\frac{5}{2} \) \( x=-\frac{1}{2} \) or \( x=\frac{5}{2} \) \( x=\frac{1}{2} \) or \( x=\frac{5}{3} \) \[ \begin{array}{l}x=\frac{5}{3} \\ x\end{array} \]

To solve the quadratic equation \( 6x^{2}-13x+5=0 \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 6 \), \( b = -13 \), and \( c = 5 \). Plugging in these values, we find \( b^2 - 4ac = (-13)^2 - 4 \times 6 \times 5 = 169 - 120 = 49 \). Therefore, \( x = \frac{13 \pm 7}{12} \), leading to the solutions \( x = \frac{20}{12} = \frac{5}{3} \) and \( x = \frac{6}{12} = \frac{1}{2} \). Fun fact: Did you know that quadratic equations date back to ancient civilizations? Babylonian mathematicians were solving equations like this more than 4,000 years ago, and their methods laid the groundwork for the algebra we use today! In real-world applications, solving quadratic equations like this can be crucial for optimizing areas or calculating projectile motion. For example, if you're trying to determine the height of a thrown ball or the area of a garden, knowing how to solve these equations can help you make the best decisions based on your calculations!