2x-x в квадрате=-8

Let's solve the equation:

\[ 2x - x^2 = -8 \]

Step 1: Rewrite the equation in standard quadratic form:

\[ -x^2 + 2x + 8 = 0 \]

Multiply both sides by -1 to make the coefficient of \(x^2\) positive:

\[ x^2 - 2x - 8 = 0 \]

Step 2: Solve the quadratic equation using the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \(a=1\), \(b=-2\), and \(c=-8\).

Step 3: Calculate the discriminant:

\[ D = b^2 - 4ac = (-2)^2 - 4 \times 1 \times (-8) = 4 + 32 = 36 \]

Step 4: Find the roots:

\[ x = \frac{-(-2) \pm \sqrt{36}}{2 \times 1} = \frac{2 \pm 6}{2} \]

So,

\[ x = \frac{2 + 6}{2} = \frac{8}{2} = 4 \]

and

\[ x = \frac{2 - 6}{2} = \frac{-4}{2} = -2 \]

Final answer:

\[ x = 4 \quad \text{or} \quad x = -2 \]