Solve for x in the quadratic equation: \( 2x^{2} + 4x - 6 = 0 \)

To solve for \( x \) in the quadratic equation \( 2x^{2} + 4x - 6 = 0 \), we can start by simplifying the equation. Divide everything by 2 to make it easier: \[ x^{2} + 2x - 3 = 0 \] Next, we can factor the quadratic: \[ (x + 3)(x - 1) = 0 \] This gives us two solutions by setting each factor to zero: \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] Therefore, the solutions are \( x = -3 \) and \( x = 1 \). For a bit of extra flair, you'll find that quadratic equations are a fantastic way to explore the world of algebra! They pop up in various scenarios, like projectile motion or profit maximization in business, making them both practical and exciting. Remember, when you solve these, it's all about finding the roots—just like digging for buried treasure!