x 2 −11x−46=−6x+4

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

1. First, let's simplify the equation by bringing all terms to one side. We can do this by adding 6x to both sides and subtracting 4 from both sides. This gives us:

   x^2 - 11x + 6x + 46 - 4 = 0

2. Simplify the equation further:

   x^2 - 5x + 42 = 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 = 1, b = -5, and c = 42.

4. Plug these values into the quadratic formula:

   x = [5 ± sqrt((-5)^2 - 4142)] / (2*1) x = [5 ± sqrt(25 - 168)] / 2

5. Since the value under the square root is negative (25 - 168 = -143), there are no real solutions for this equation. The solutions are complex numbers.

So, the equation x^2 - 5x + 42 = 0 has no real solutions.