12. \( 3 x^{2}=75 \)

To solve the equation \( 3 x^{2}=75 \), first, divide both sides by 3 to simplify it. This gives you \( x^{2} = 25 \). From there, you take the square root of both sides, which leads to \( x = 5 \) or \( x = -5 \). So, your solutions are \( x = 5 \) and \( x = -5 \)! Now let's make it real! Quadratic equations pop up in various fields, from physics describing projectile motion to economics modeling profit-maximizing scenarios. So, knowing how to handle \( ax^2 + bx + c = 0 \) can be your secret weapon in tackling real-world problems and analyses! And remember, a common mistake is forgetting to take both the positive and negative square roots when solving for \( x \). It’s like forgetting to add the cherry on top of a sundae – it’s just not complete without it! Always check your solutions by plugging them back into the original equation!