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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-50x^2)/200x^2+40x/200x^2+(-20x)/200x^2+2=0

We multiply all the terms by the denominator


(-50x^2)+40x+(-20x)+2*200x^2=0

Wy multiply elements

(-50x^2)+400x^2+40x+(-20x)=0

We get rid of parentheses

-50x^2+400x^2+40x-20x=0

We add all the numbers together, and all the variables

350x^2+20x=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*350}=\frac{-40}{700}
=-2/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$