X²-4/8-2x+3/3=-1

To solve the equation x² - 4/8 - 2x + 3/3 = -1, we can start by simplifying the equation:

x² - 1/2 - 2x + 1 = -1

x² - 2x - 1/2 = -2

Now, let's move all the terms to one side of the equation to obtain a quadratic equation:

x² - 2x - 1/2 + 2 = 0

x² - 2x + 3/2 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Since this equation is not easily factorable, let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 1, b = -2, and c = 3/2. Substituting these values into the quadratic formula:

x = (-(-2) ± √((-2)² - 4(1)(3/2))) / (2(1))

x = (2 ± √(4 - 6)) / 2

x = (2 ± √(-2)) / 2

Since we have a square root of a negative number, this equation does not have real solutions. Therefore, the equation x² - 4/8 - 2x + 3/3 = -1 has no solution.