2y+4/y=9

Solution for 2y+4/y=9 equation:

2y+4/y=9

We move all terms to the left:

2y+4/y-(9)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


2y*y-9*y+4=0

We add all the numbers together, and all the variables

-9y+2y*y+4=0

Wy multiply elements

2y^2-9y+4=0

a = 2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·2·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*2}=\frac{2}{4}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*2}=\frac{16}{4}
=4
$