2/x-1/x+1=-2/5x+5

Solution for 2/x-1/x+1=-2/5x+5 equation:

2/x-1/x+1=-2/5x+5

We move all terms to the left:

2/x-1/x+1-(-2/5x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+5)!=0

x∈R


We get rid of parentheses

2/x-1/x+2/5x-5+1=0

We calculate fractions


(-5x+2)/5x^2+2x/5x^2-5+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-20x^2+2x+(-5x+2)=0

We get rid of parentheses

-20x^2+2x-5x+2=0

We add all the numbers together, and all the variables

-20x^2-3x+2=0

a = -20; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-20)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-20}=\frac{-10}{-40}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-20}=\frac{16}{-40}
=-2/5
$