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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+x*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
$