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

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Answer 1 · 2015-07-22T12:29:05

Similar to the case of a quadratic equation.

For example, the equation

$4x^2 - 5x = 6$ has roots $x = 2$ and $x = -3/4$ which may be written as,

$(x - 2)(4x + 3) = 0$

Thus, coming to the case of an inequation,

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

$x < 2$ and $x < -3/4$

How do you solve quadratic inequalities 4x^2 - 5x < 64x^2 - 5x < 6?