2x+4/x=9

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

2x+4/x=9

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-9x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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