Final answer:
To solve the quadratic equation x² + 4x + 20 = 12x - 5, we need to bring all terms to one side and set it equal to zero. Simplifying, we get x² - 8x + 25 = 0. By applying the quadratic formula, we find that there are no real solutions to this equation.
Step-by-step explanation:
This expression is a quadratic equation of the form x² + 4x + 20 = 12x - 5. To solve this equation, we need to bring all terms to one side and set it equal to zero. x² + 4x + 20 - 12x + 5 = 0. Simplifying, we get x² - 8x + 25 = 0.
We can now solve this quadratic equation using the quadratic formula, which states that the solutions are given by x = (-b ± √(b² - 4ac)) / (2a). In this case, a = 1, b = -8, and c = 25. Substituting these values into the formula, we get x = (8 ± √((-8)² - 4(1)(25))) / (2(1)).
Simplifying further, we have x = (8 ± √(64 - 100)) / 2. Since the expression under the square root is negative, there are no real solutions to this quadratic equation. Therefore, the equation has no solution.