Final answer:
To solve the equation 12x-4x²+9, we can use the quadratic formula to find the solutions for x. The solutions are x = (-12 ± 12√2)/(8) and x = (-3 ± 3√2)/(2).
Step-by-step explanation:
To find the solution to the expression 12x-4x²+9, we need to set the expression equal to zero and solve for x.
We can rewrite the expression as -4x² + 12x + 9 = 0.
Next, we can solve the quadratic equation by factoring, completing the square, or using the quadratic formula.
For this particular equation, factoring does not yield real roots, nor does completing the square. Therefore, we can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by x = (-b ± √(b²-4ac))/(2a). Plugging in the values from our equation, we get x = (-12 ± √(12² - 4(-4)(9)))/(2(-4)). Simplifying further, we have x = (-12 ± √(144 + 144))/(8) and x = (-12 ± √(288))/(8). Lastly, we can simplify the square root to x = (-12 ± 12√2)/(8) and x = (-3 ± 3√2)/(2). These are the solutions to the equation.