# What is x if 2/x-3x=-4?

Mar 7, 2016

$\frac{2 \pm \sqrt{10}}{3}$

#### Explanation:

$\frac{2}{x} - 3 x = - 4$
$\mathmr{and} 2 - 3 {x}^{2} = - 4 x$
$\mathmr{and} 3 {x}^{2} - 4 x - 2 = 0$

which is in the standard quadratic form:
$a {x}^{2} + b x + c = 0$

where b = -4, a = 3, c = -2
Hence, the roots of the equation are given by:
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$\mathmr{and} x = \left(\frac{4 \pm \sqrt{16 + 24}}{6}\right)$
$\mathmr{and} x = \frac{4 \pm \sqrt{40}}{6}$
$\mathmr{and} x = \frac{2 \pm \sqrt{10}}{3}$