Determine the value of 'x' that satisfies the equation: $8=x^{2}-5 x+8$

Step 1 ：We are given the equation \(8=x^{2}-5 x+8\). This is a quadratic equation, which is in the general form \(ax^2 + bx + c = 0\).

Step 2 ：The solutions to a quadratic equation can be found using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 3 ：In this case, a = 1, b = -5, and c = 8. We can substitute these values into the quadratic formula to find the solutions for x.

Step 4 ：However, before we do that, we need to calculate the discriminant, D, which is given by \(D = b^2 - 4ac\).

Step 5 ：Substituting the values of a, b, and c, we find that \(D = (-5)^2 - 4*1*8 = -7\).

Step 6 ：The discriminant is negative, which means that the equation has no real solutions. The solutions are complex numbers.

Step 7 ：\(\boxed{\text{The equation } 8=x^{2}-5 x+8 \text{ has no real solutions.}}\)