We need to solve the quadratic equations $x^2 - 9x + 20 = 0$ and $3x^2 + 8x + 4 = 0$ by graphing.

1. Problem Description

We need to solve the quadratic equations $x^2 - 9x + 20 = 0$ and $3x^2 + 8x + 4 = 0$ by graphing.

2. Solution Steps

Problem 27: $x^2 - 9x + 20 = 0$

We can factorize the quadratic equation:

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

Therefore, the roots are $x = 4$ and $x = 5$.

The solutions are the $x$-intercepts of the graph of the equation $y = x^2 - 9x + 20$. The $x$-intercepts occur when $y = 0$.

Thus, the solutions are $x = 4$ and $x = 5$.

Problem 28: $3x^2 + 8x + 4 = 0$

We can factorize the quadratic equation:

$3x^2 + 8x + 4 = (3x + 2)(x + 2) = 0$

Therefore, the roots are $x = -\frac{2}{3}$ and $x = -2$.

The solutions are the $x$-intercepts of the graph of the equation $y = 3x^2 + 8x + 4$. The $x$-intercepts occur when $y = 0$.

Thus, the solutions are $x = -\frac{2}{3}$ and $x = -2$.

3. Final Answer

For problem 27:

$x = 4, 5$

For problem 28:

$x = -\frac{2}{3}, -2$