1/4x+1/5=1/20x

Solution for 1/4x+1/5=1/20x equation:

1/4x+1/5=1/20x

We move all terms to the left:

1/4x+1/5-(1/20x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(+1/20x)+1/5=0

We get rid of parentheses

1/4x-1/20x+1/5=0

We calculate fractions


160x^2/2000x^2+500x/2000x^2+(-100x)/2000x^2=0

We multiply all the terms by the denominator


160x^2+500x+(-100x)=0

We get rid of parentheses

160x^2+500x-100x=0

We add all the numbers together, and all the variables

160x^2+400x=0

a = 160; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·160·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*160}=\frac{-800}{320}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*160}=\frac{0}{320}
=0
$