2x 2 −8x+12=−3x

Sure, let's solve the equation step by step:

1. First, let's bring all terms to one side of the equation. We add 3x to both sides to get rid of -3x on the right side:

   2x^2 - 8x + 3x + 12 = 0

2. Simplify the equation:

   2x^2 - 5x + 12 = 0

3. Now, we need to solve for x. This is a quadratic equation, so we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 2, b = -5, and c = 12.

4. Plug a, b, and c into the formula:

   x = [5 ± sqrt((-5)^2 - 4212)] / (2*2)

5. Simplify under the square root:

   x = [5 ± sqrt(25 - 96)] / 4

6. Since the value under the square root is negative (25 - 96 = -71), there are no real solutions for this equation. The solutions are complex numbers.

So, the equation 2x^2 - 8x + 12 = -3x has no real solutions.