Solve for the roots in simplest form using the quadratic formula: \[ 4 x^{2}-20 x=-13 \]

To solve the quadratic equation \( 4x^{2} - 20x = -13 \) using the quadratic formula, follow these steps: 1. **Rewrite the equation in standard form:** \[ 4x^{2} - 20x + 13 = 0 \] 2. **Identify the coefficients:** \[ a = 4, \quad b = -20, \quad c = 13 \] 3. **Apply the quadratic formula:** \[ x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \] 4. **Plug in the values of \( a \), \( b \), and \( c \):** \[ x = \frac{20 \pm \sqrt{(-20)^{2} - 4 \cdot 4 \cdot 13}}{2 \cdot 4} \] \[ x = \frac{20 \pm \sqrt{400 - 208}}{8} \] \[ x = \frac{20 \pm \sqrt{192}}{8} \] 5. **Simplify the square root:** \[ \sqrt{192} = \sqrt{64 \cdot 3} = 8\sqrt{3} \] 6. **Substitute back into the equation:** \[ x = \frac{20 \pm 8\sqrt{3}}{8} \] 7. **Simplify the expression by dividing numerator and denominator by 4:** \[ x = \frac{5 \pm 2\sqrt{3}}{2} \] **Final Answer:** \[ x = \frac{5 \pm 2\sqrt{3}}{2} \]