# How do you solve quadratic inequalities 4x^2 - 5x < 6?

##### 1 Answer
Jul 22, 2015

Similar to the case of a quadratic equation.

#### Explanation:

For example, the equation

$4 {x}^{2} - 5 x = 6$ has roots $x = 2$ and $x = - \frac{3}{4}$ which may be written as,

$\left(x - 2\right) \left(4 x + 3\right) = 0$

Thus, coming to the case of an inequation,

$\left(x - 2\right) \left(4 x + 3\right) < 0$
which naturally implies,

$x < 2$ and $x < - \frac{3}{4}$