x²-9x+20=0

To solve the quadratic equation \( x^2 - 9x + 20 = 0 \), we can factor it. We need to find two numbers that multiply to \( 20 \) (the constant term) and add up to \( -9 \) (the coefficient of \( x \)).

The two numbers that meet these criteria are \( -4 \) and \( -5 \). So we can factor the quadratic as follows:

\[ (x - 4)(x - 5) = 0 \]

Now, we can set each factor to zero:

1. \( x - 4 = 0 \) → \( x = 4 \)
2. \( x - 5 = 0 \) → \( x = 5 \)

Therefore, the solutions to the equation \( x^2 - 9x + 20 = 0 \) are:

\[ x = 4 \quad \text{and} \quad x = 5 \]