Question 10 Solve for \( x: 6 x^{2}-5 x-4=0 \) Important: Be sure to submit in order from least to greatest! \( x= \) Blank 1 \( x= \) Blank 2

**Step 1: Write Down the Equation** We start with the quadratic equation \[ 6x^2 - 5x - 4 = 0. \] **Step 2: Identify the Coefficients** The coefficients are: \[ a = 6, \quad b = -5, \quad c = -4. \] **Step 3: Apply the Quadratic Formula** The quadratic formula is \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \] Substitute the coefficients into the formula: \[ x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(6)(-4)}}{2(6)}. \] **Step 4: Simplify the Expression** Simplify the numerator and the discriminant: \[ x = \frac{5 \pm \sqrt{25 + 96}}{12}. \] \[ x = \frac{5 \pm \sqrt{121}}{12}. \] **Step 5: Compute the Square Root** Since \(\sqrt{121} = 11\), the expression becomes: \[ x = \frac{5 \pm 11}{12}. \] **Step 6: Find the Two Solutions** Calculate each solution separately: For the negative branch: \[ x = \frac{5 - 11}{12} = \frac{-6}{12} = -\frac{1}{2}. \] For the positive branch: \[ x = \frac{5 + 11}{12} = \frac{16}{12} = \frac{4}{3}. \] **Step 7: Write the Final Answers in Order (Least to Greatest)** Blank 1: \[ x = -\frac{1}{2} \] Blank 2: \[ x = \frac{4}{3} \]