Solve the equation using the quadrati \[ \begin{array}{l}x(5 x+6)=-7\end{array} \]

To solve the equation \( x(5x + 6) = -7 \), we first rewrite it in standard form: 1. Expand the left side: \[ 5x^2 + 6x + 7 = 0 \] 2. Now we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 5 \), \( b = 6 \), and \( c = 7 \). 3. Calculate the discriminant: \[ b^2 - 4ac = 6^2 - 4 \cdot 5 \cdot 7 = 36 - 140 = -104 \] Since the discriminant is negative, this means there are no real solutions, but we can find complex solutions. 4. Use the quadratic formula: \[ x = \frac{-6 \pm \sqrt{-104}}{10} \] \[ x = \frac{-6 \pm \sqrt{104}i}{10} \] \[ x = \frac{-6 \pm 2\sqrt{26}i}{10} \] \[ x = \frac{-3 \pm \sqrt{26}i}{5} \] So, the solutions to the equation are: \[ x = \frac{-3 + \sqrt{26}i}{5} \quad \text{and} \quad x = \frac{-3 - \sqrt{26}i}{5} \]