# How do you multiply 2y + 3 / y = 3/2?

Jun 21, 2015
• Equation obtained after multiplying:
color(red)(4y^2 - 3 y+6=0
• The solution:
color(red)( (3+-sqrt(-87))/8

#### Explanation:

$2 y + \frac{3}{y} = \frac{3}{2}$
Taking L.C.M on the L.H.S

(2y^2 + 3) / y =color(green)( 3/2

Cross multiplying

(2y^2 + 3) . color(green)(2 )= 3 . color(green)(y
$4 {y}^{2} + 6 = 3 y$
color(red)(4y^2 - 3 y+6=0

solving the equation :
The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(- 3\right)}^{2} - \left(4 \cdot \left(4\right) \cdot 6\right)$

$= 9 - 96 = - 87$
As, $\Delta < 0$ there are complex solutions

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

As $\Delta = - 87$, x = (-(-3)+-sqrt(-87))/(2*4) =color(red)( (3+-sqrt(-87))/8