We are asked to solve the quadratic equation $x^2 - 9x + 20 = 0$ by graphing. This means we want to find the $x$-intercepts of the graph of the quadratic function $y = x^2 - 9x + 20$.

1. Problem Description

We are asked to solve the quadratic equation $x^2 - 9x + 20 = 0$ by graphing. This means we want to find the $x$-intercepts of the graph of the quadratic function $y = x^2 - 9x + 20$.

2. Solution Steps

First, we can create a table of values for $y = x^2 - 9x + 20$:

x | y

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3 | $3^2 - 9(3) + 20 = 9 - 27 + 20 = 2$

4 | $4^2 - 9(4) + 20 = 16 - 36 + 20 = 0$

5 | $5^2 - 9(5) + 20 = 25 - 45 + 20 = 0$

6 | $6^2 - 9(6) + 20 = 36 - 54 + 20 = 2$

From the table, we can see that the function has roots at $x=4$ and $x=5$. These are the $x$-intercepts of the graph. We can also solve this by factoring the quadratic:

$x^2 - 9x + 20 = (x-4)(x-5) = 0$.

Therefore $x-4 = 0$ or $x-5 = 0$, so $x=4$ or $x=5$.

3. Final Answer

$x = 4, 5$