1/2x+2/5=1/10x

Solution for 1/2x+2/5=1/10x equation:

1/2x+2/5=1/10x

We move all terms to the left:

1/2x+2/5-(1/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/10x)+2/5=0

We get rid of parentheses

1/2x-1/10x+2/5=0

We calculate fractions


40x^2/500x^2+250x/500x^2+(-50x)/500x^2=0

We multiply all the terms by the denominator


40x^2+250x+(-50x)=0

We get rid of parentheses

40x^2+250x-50x=0

We add all the numbers together, and all the variables

40x^2+200x=0

a = 40; b = 200; c = 0;
Δ = b2-4ac
Δ = 2002-4·40·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200}{2*40}=\frac{-400}{80}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200}{2*40}=\frac{0}{80}
=0
$