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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x+1x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-x+()/10x+5x/10x-1=0

We add all the numbers together, and all the variables

-1x+()/10x+5x/10x-1=0

We multiply all the terms by the denominator


-1x*10x+5x-1*10x+()=0

We add all the numbers together, and all the variables

5x-1x*10x-1*10x=0

Wy multiply elements

-10x^2+5x-10x=0

We add all the numbers together, and all the variables

-10x^2-5x=0

a = -10; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-10)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-10}=\frac{10}{-20}
=-1/2
$