Solve for \( u \) : \[ 3 u^{2}+10 u-13=0 \] Answer: \( u=\square \) \( u=\square \)

To solve the quadratic equation \( 3 u^{2} + 10 u - 13 = 0 \), we can use the quadratic formula \( u = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 3 \), \( b = 10 \), and \( c = -13 \). First, we calculate the discriminant: \[ b^2 - 4ac = 10^2 - 4 \cdot 3 \cdot (-13) = 100 + 156 = 256 \] Now, substituting back into the formula: \[ u = \frac{-10 \pm \sqrt{256}}{2 \cdot 3} = \frac{-10 \pm 16}{6} \] This gives us two possible solutions: 1. \( u = \frac{6}{6} = 1 \) 2. \( u = \frac{-26}{6} = -\frac{13}{3} \) So the solutions are: \[ u = 1 \] \[ u = -\frac{13}{3} \]