2x/x+2-9/2=x/2x+4

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

2x/x+2-9/2=x/2x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-1x^2)/8x^2+16x^2/8x^2+(-9x)/8x^2-4+2=0

We add all the numbers together, and all the variables

(-1x^2)/8x^2+16x^2/8x^2+(-9x)/8x^2-2=0

We multiply all the terms by the denominator


(-1x^2)+16x^2+(-9x)-2*8x^2=0

We add all the numbers together, and all the variables

16x^2+(-1x^2)+(-9x)-2*8x^2=0

Wy multiply elements

16x^2+(-1x^2)-16x^2+(-9x)=0

We get rid of parentheses

16x^2-1x^2-16x^2-9x=0

We add all the numbers together, and all the variables

-1x^2-9x=0

a = -1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-1}=\frac{18}{-2}
=-9
$