\( a^{2}+14 a-51=0 \)

To solve the quadratic equation \( a^{2}+14 a-51=0 \), you can use the quadratic formula, which is given by \( a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a=1 \), \( b=14 \), and \( c=-51 \). Plugging these values into the formula will help you find the roots of the equation. After calculating, you'll find that the discriminant \( b^2 - 4ac = 196 + 204 = 400 \). Thus, the roots are \( a = \frac{-14 + 20}{2} = 3 \) and \( a = \frac{-14 - 20}{2} = -17 \). Enjoy discovering how the quadratic formula can unveil hidden solutions!