Solve for \(x\) in the equation \(2x^2 - 8x + 6 = 0\) using the quadratic formula.

["Solving (2x^2 - 8x + 6 = 0) Using the Quadratic Formula: A Step-by-Step Guide", "Quadratic equations are fundamental in algebra, and knowing how to solve them efficiently is essential for students and math enthusiasts alike. One of the most reliable methods is the quadratic formula, which provides an elegant solution for equations of the form (ax^2 + bx + c = 0). In this article, we’ll solve the equation (2x^2 - 8x + 6 = 0) using the quadratic formula, offering clear, step-by-step guidance to help you master this powerful technique.", "---", "### What is the Quadratic Formula?", "The quadratic formula solves equations (ax^2 + bx + c = 0) via:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Where:\n- (a), (b), and (c) are coefficients from the equation\n- The discriminant, (D = b^2 - 4ac), determines the nature of the roots (real and distinct, real and repeated, or imaginary)", "---", "### Step 1: Identify Coefficients", "Given the equation:", "[\n2x^2 - 8x + 6 = 0\n]", "We identify:\n(a = 2),\n(b = -8),\n(c = 6)", "---", "### Step 2: Compute the Discriminant", "[\nD = b^2 - 4ac = (-8)^2 - 4(2)(6) = 64 - 48 = 16\n]", "Since (D = 16 > 0), there are two distinct real solutions. This confirms the quadratic formula will yield two real values.", "---", "### Step 3: Apply the Quadratic Formula", "Substitute (a = 2), (b = -8), and (c = 6) into the formula:", "[\nx = \frac{-(-8) \pm \sqrt{16}}{2(2)} = \frac{8 \pm 4}{4}\n]", "---", "### Step 4: Solve for Both Roots", "[\nx_1 = \frac{8 + 4}{4} = \frac{12}{4} = 3\n]", "[\nx_2 = \frac{8 - 4}{4} = \frac{4}{4} = 1\n]", "---", "### Conclusion", "The solutions to the quadratic equation (2x^2 - 8x + 6 = 0) are:", "[\nx = 3 \quad \ ext{and} \quad x = 1\n]", "Using the quadratic formula ensures accuracy, especially with more complex coefficients, and saves time compared to factoring or completing the square. Mastering this method empowers students to confidently solve quadratic equations—key for algebra, calculus, and real-world applications.", "---", "### Pro Tips\n- Always compute the discriminant first to understand the nature of the roots.\n- Keep signs clear: (b = -8) leads to (-b = +8).\n- Simplify fractions carefully to avoid arithmetic errors.", "Start practicing today—solving (2x^2 - 8x + 6 = 0) (and others like it) has never been easier!", "---", "Keywords: quadratic formula, solve quadratic equations, (2x^2 - 8x + 6 = 0), math tutorial, algebra solutions, discriminant, real roots, step-by-step equation solving"]