Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 2\), \(b = -16\), \(c = 30\).

["# Solving Quadratic Equations Made Easy with the Quadratic Formula", "When it comes to solving quadratic equations of the form (ax^2 + bx + c = 0), the quadratics formula stands as a reliable and powerful tool. For students, educators, and math enthusiasts alike, mastering this formula unlocks quick and accurate solutions. In this article, we’ll explore how to apply the quadratic formula using specific coefficients — (a = 2), (b = -16), and (c = 30) — step by step.", "---", "## What Is the Quadratic Formula?", "The quadratic formula is:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "This equation provides the solutions (roots) for any quadratic equation, helping determine where the parabola intersects the x-axis. The discriminant (D = b^2 - 4ac) reveals critical information: whether the roots are real or complex, and whether they are distinct or repeated.", "---", "## Step-by-Step: Solving (2x^2 - 16x + 30 = 0)", "### Step 1: Identify coefficients\nFrom the equation (2x^2 - 16x + 30 = 0), extract:\n- (a = 2)\n- (b = -16)\n- (c = 30)", "### Step 2: Compute the discriminant\n[\nD = b^2 - 4ac = (-16)^2 - 4(2)(30) = 256 - 240 = 16\n]\nSince (D = 16 > 0), there are two distinct real roots.", "### Step 3: Apply the quadratic formula\n[\nx = \frac{-(-16) \pm \sqrt{16}}{2 \ imes 2} = \frac{16 \pm 4}{4}\n]", "### Step 4: Calculate both solutions\n- First root:\n[\nx_1 = \frac{16 + 4}{4} = \frac{20}{4} = 5\n]\n- Second root:\n[\nx_2 = \frac{16 - 4}{4} = \frac{12}{4} = 3\n]", "---", "## Final Answer", "The solutions to the quadratic equation (2x^2 - 16x + 30 = 0) are:\n[\nx = 5 \quad \ ext{and} \quad x = 3\n]", "---", "## Why Use the Quadratic Formula?", "- Universal Application: Works for any quadratic equation, regardless of how easily it factors.\n- Quick Resolution: Saves time compared to factoring or completing the square.\n- Insight into Roots: The discriminant clarifies root nature—real and distinct, real and repeated, or complex.\n- Essential Skill: Foundational for algebra, physics, engineering, and computer science.", "---", "## Conclusion", "Using the quadratic formula (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}) is a straightforward yet powerful method to solve quadratic equations. With coefficients (a = 2), (b = -16), and (c = 30), we found two simple real roots: (x = 3) and (x = 5). Practice with diverse equations will boost your fluency and confidence in this cornerstone mathematical technique.", "---", "Keywords: quadratic formula, solving quadratic equations, x = (-b ± √(b²−4ac))/2a, discriminant calculation, real roots, quadratic solutions, algebra tutorial, math formula application."]