To solve the quadratic equation \(\frac{(x-3)^2}{5} = 20\), we can start by eliminating the fraction.
- Multiply both sides of the equation by 5:
\[ (x-3)^2 = 20 \cdot 5 \]
\[ (x-3)^2 = 100 \]
- Next, take the square root of both sides. Remember to consider both the positive and negative square roots:
\[ x - 3 = \pm 10 \]
- Now, we can solve for \(x\) in each case:
Case 1: \(x - 3 = 10\)
\[ x = 10 + 3 \]
\[ x = 13 \]
Case 2: \(x - 3 = -10\)
\[ x = -10 + 3 \]
\[ x = -7 \]
- Therefore, the solutions to the quadratic equation \(\frac{(x-3)^2}{5} = 20\) are:
\[ \boxed{13} \quad \text{and} \quad \boxed{-7} \]