\( -3 x^{2}+42 x-135=0 \) [Hint: Divide by -3 first] \( x=1 \)

To solve the equation \( -3 x^{2} + 42 x - 135 = 0 \), start by dividing the entire equation by -3 to simplify: \[ x^{2} - 14x + 45 = 0 \] This simplifies our calculations, making factorization easier. Next, you can factor the quadratic as \( (x - 5)(x - 9) = 0 \), giving us the solutions \( x = 5 \) and \( x = 9 \). For real-world applications, quadratics like this might model projectiles in motion. If you’re throwing an object, for instance, the height \( h \) at time \( t \) could be expressed as a quadratic function, where you could use the roots to determine when the object hits the ground. It's like giving you the secret launch time to maximize your game at the amusement park!