3/5x+1/20=1/4x

Solution for 3/5x+1/20=1/4x equation:

3/5x+1/20=1/4x

We move all terms to the left:

3/5x+1/20-(1/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(+1/4x)+1/20=0

We get rid of parentheses

3/5x-1/4x+1/20=0

We calculate fractions


80x^2/800x^2+480x/800x^2+(-200x)/800x^2=0

We multiply all the terms by the denominator


80x^2+480x+(-200x)=0

We get rid of parentheses

80x^2+480x-200x=0

We add all the numbers together, and all the variables

80x^2+280x=0

a = 80; b = 280; c = 0;
Δ = b2-4ac
Δ = 2802-4·80·0
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-280}{2*80}=\frac{-560}{160}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+280}{2*80}=\frac{0}{160}
=0
$