9/5x-2=2/x+2

Solution for 9/5x-2=2/x+2 equation:

9/5x-2=2/x+2

We move all terms to the left:

9/5x-2-(2/x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

9/5x-2/x-2-2=0

We calculate fractions


9x/5x^2+(-10x)/5x^2-2-2=0

We add all the numbers together, and all the variables

9x/5x^2+(-10x)/5x^2-4=0

We multiply all the terms by the denominator


9x+(-10x)-4*5x^2=0

Wy multiply elements

-20x^2+9x+(-10x)=0

We get rid of parentheses

-20x^2+9x-10x=0

We add all the numbers together, and all the variables

-20x^2-1x=0

a = -20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-20)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-20}=\frac{2}{-40}
=-1/20
$