求满足 $5x^2 + 12x > 3x + 2$ 的 $x$ 的取值范围。

1. Rearrange the inequality into standard quadratic form

$5x^2 + 12x - 3x - 2 > 0$
$5x^2 + 9x - 2 > 0$

2. Factorise the quadratic expression

$(5x - 1)(x + 2) > 0$

3. Determine the range of values for x

The roots of the equation $(5x - 1)(x + 2) = 0$ are $x = \frac{1}{5}$ and $x = -2$.
Since the inequality is $> 0$ and the coefficient of $x^2$ is positive, the solution is $x < -2$ or $x > \frac{1}{5}$.