17. Which value(s) of \( x \) satisfies the equation below? \[ 11 x^{2}-12 x+3=6 x^{2}-1 \] a. \( \left\{-\frac{2}{5},-2\right\} \) b. \( \left\{\frac{2}{5}, 2\right\} \) c. \( \{5,-2\} \) d. \( \left\{\frac{2}{5}, 5\right\} \)

First, we can simplify the equation by moving all terms to one side: \[ 11x^2 - 12x + 3 - 6x^2 + 1 = 0 \] This simplifies to: \[ 5x^2 - 12x + 4 = 0 \] Now, we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 5 \), \( b = -12 \), and \( c = 4 \). Plugging in these values gives: \[ x = \frac{12 \pm \sqrt{(-12)^2 - 4 \cdot 5 \cdot 4}}{2 \cdot 5} \] Calculating the discriminant: \[ 144 - 80 = 64 \] Now substituting back: \[ x = \frac{12 \pm 8}{10} \] This results in two solutions: 1. \( x = \frac{20}{10} = 2 \) 2. \( x = \frac{4}{10} = \frac{2}{5} \) Thus, the values of \( x \) that satisfy the equation are \( \left\{\frac{2}{5}, 2\right\} \). So the correct answer is **b. \( \left\{\frac{2}{5}, 2\right\} \)**.