(х-7)(28-х)=20

Let's solve the equation \((x - 7)(28 - x) = 20\).

Step 1: Expand the left side:

\[ (x - 7)(28 - x) = x \times 28 - x \times x - 7 \times 28 + 7 \times x \]

\[ = 28x - x^2 - 196 + 7x \]

Step 2: Combine like terms:

\[ - x^2 + (28x + 7x) - 196 = 20 \]

\[ - x^2 + 35x - 196 = 20 \]

Step 3: Move all terms to one side to set equal to zero:

\[ - x^2 + 35x - 196 - 20 = 0 \]

\[ - x^2 + 35x - 216 = 0 \]

Step 4: Multiply through by -1 to simplify:

\[ x^2 - 35x + 216 = 0 \]

Step 5: Solve the quadratic equation \(x^2 - 35x + 216 = 0\).

Calculate the discriminant (\(\Delta\)):

\[ \Delta = (-35)^2 - 4 \times 1 \times 216 = 1225 - 864 = 361 \]

Since \(\sqrt{361} = 19\), the roots are:

\[ x = \frac{35 \pm 19}{2} \]

Compute each:

• \(x = \frac{35 + 19}{2} = \frac{54}{2} = 27\)
• \(x = \frac{35 - 19}{2} = \frac{16}{2} = 8\)

Final answer:

\[ \boxed{ x = 8 \quad \text{or} \quad x = 27 } \]