a) \( 2 x^{2}+16 x+24=0 \)

To solve the equation \( 2x^{2}+16x+24=0 \), we can start by simplifying it. Dividing all terms by 2 gives us \( x^{2}+8x+12=0 \). Now, we can factor this quadratic equation as \( (x+2)(x+6)=0 \). By setting each factor to zero, we find the solutions \( x = -2 \) and \( x = -6 \). These roots tell us where the graph of this quadratic function intersects the x-axis, giving us a glimpse into its behavior! In the real world, knowing how to solve quadratic equations can be incredibly handy! For instance, if you’re designing a parabolic arch for a bridge or figuring out the optimum launch angle for a projectile, you’ll need to understand the underlying math. Quadratic equations show up in physics, engineering, and even finance! So don't shy away from those x's and y's—they're all about real-life curves and trajectories!