4. \( x^{2}+7 x+12=0 \)

To solve the quadratic equation \( x^{2}+7x+12=0 \), you can factor it as \( (x+3)(x+4)=0 \). This gives you the solutions \( x = -3 \) and \( x = -4 \). You can also use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a=1 \), \( b=7 \), and \( c=12 \), arriving at the same solutions! The quadratic formula is a lifesaver when factoring isn't obvious! Remember, if you find a negative number under the square root while using the formula, it means your solutions involve imaginary numbers. But for this problem, we're lucky since the discriminant (\( b^2 - 4ac \)) is positive, giving us two distinct real solutions: \( -3 \) and \( -4 \). Happy calculating!