# How do you solve 1/2 - 3/2x = 4/x - 5/12?

Oct 1, 2015

The equation doesn't have a real solution

#### Explanation:

Multiply both sides by $12 x$ (which is the LCM of 2, 12 and x)

$6 x - 18 {x}^{2} = 48 - 5 x$

Make one of the sides equal zero,

$- 18 {x}^{2} + 11 x - 48 = 0$
$18 {x}^{2} - 11 x + 48 = 0$

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 18 \cdot 48}}{36} = \frac{11 \pm \sqrt{- 3335}}{36}$