Una ecuación cuadrática está dada por \( 2x^2 - 4x - 6 = 0 \). ¿Cuáles son sus raíces?

["SEO Title: Solve ( 2x^2 - 4x - 6 = 0 ): Step-by-Step Guide to Finding Its Roots", "Meta Description:\nLearn how to solve the quadratic equation ( 2x^2 - 4x - 6 = 0 ) using the quadratic formula. Discover the roots, their meaning, and how this applies to real-world problems.", "---", "### Understanding Quadratic Equations: A Closer Look at ( 2x^2 - 4x - 6 = 0 )", "Quadratic equations are fundamental in algebra and appear frequently in science, engineering, and everyday problem-solving. One such well-known equation is:", "[\n2x^2 - 4x - 6 = 0\n]", "But how do you find the values of ( x ) (called roots) that satisfy this equation? More importantly, what do these roots mean? In this article, we’ll solve ( 2x^2 - 4x - 6 = 0 ) step-by-step and explore their significance.", "---", "### Why Solve Quadratic Equations?", "Before jumping into calculations, consider why solving quadratics matters. They model:", "- Projectile motion\n- Optimization problems\n- Economic trends\n- Area-related challenges\n- Physics and engineering equations", "So mastering methods to find roots gives you a powerful tool for modeling and solving real-world issues.", "---", "### Step 1: Simplify the Equation (if possible)", "The given equation is:\n[\n2x^2 - 4x - 6 = 0\n]", "Notice all coefficients are divisible by 2. We can simplify by dividing the entire equation by 2:", "[\nx^2 - 2x - 3 = 0\n]", "Now we solve the simpler equation:\n[\nx^2 - 2x - 3 = 0\n]", "---", "### Step 2: Use the Quadratic Formula", "For any quadratic equation of the form ( ax^2 + bx + c = 0 ), the roots are given by:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "For our simplified equation ( x^2 - 2x - 3 = 0 ):\n- ( a = 1 )\n- ( b = -2 )\n- ( c = -3 )", "Plug values into the formula:", "[\nx = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-3)}}{2(1)}\n]\n[\nx = \frac{2 \pm \sqrt{4 + 12}}{2}\n]\n[\nx = \frac{2 \pm \sqrt{16}}{2}\n]\n[\nx = \frac{2 \pm 4}{2}\n]", "---", "### Step 3: Calculate the Roots", "Compute both possibilities:", "1. ( x = \frac{2 + 4}{2} = \frac{6}{2} = 3 )\n2. ( x = \frac{2 - 4}{2} = \frac{-2}{2} = -1 )", "---", "### Final Answer", "The roots of ( 2x^2 - 4x - 6 = 0 ) are:", "[\n\boxed{x = 3 \quad \ ext{and} \quad x = -1}\n]", "---", "### Verifying the Roots", "Always check your roots by plugging them back into the original equation:", "- For ( x = 3 ):\n ( 2(3)^2 - 4(3) - 6 = 2(9) - 12 - 6 = 18 - 12 - 6 = 0 ) ✅", "- For ( x = -1 ):\n ( 2(-1)^2 - 4(-1) - 6 = 2(1) + 4 - 6 = 2 + 4 - 6 = 0 ) ✅", "---", "### Key Takeaways", "- Quadratic equations always have two roots (real or complex).\n- Simplifying before solving saves time and reduces errors.\n- The quadratic formula works universally — even when simplification isn’t obvious.\n- Roots represent x-coordinates where the parabola intersects the x-axis.", "---", "### Related Searches", "- How to solve quadratic equations step-by-step\n- Quadratic formula explained with examples\n- How to find roots of ( 2x^2 - 4x - 6 = 0 <br/>\n- Applications of quadratic equations in real life", "---", "Ready to solve your quadratic equations? Use the formula, simplify first, and verify! Understanding the roots of ( 2x^2 - 4x - 6 = 0 ) helps unlock deeper math confidence and problem-solving skills.", "---", "Keywords: quadratic equation ( 2x^2 - 4x - 6 = 0 ), solving quadratics, quadratic formula, roots of equations, algebra tutorial, solving quadratic equations step-by-step, real-world quadratic applications.", "---", "By breaking down the problem clearly and walking through each step, readers gain not just the answer but also insight — essential for mastering algebra!"]