2/5x+1/20=3/4x

Solution for 2/5x+1/20=3/4x equation:

2/5x+1/20=3/4x

We move all terms to the left:

2/5x+1/20-(3/4x)=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

2/5x-(+3/4x)+1/20=0

We get rid of parentheses

2/5x-3/4x+1/20=0

We calculate fractions


80x^2/800x^2+320x/800x^2+(-600x)/800x^2=0

We multiply all the terms by the denominator


80x^2+320x+(-600x)=0

We get rid of parentheses

80x^2+320x-600x=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{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+280}{2*80}=\frac{560}{160}
=3+1/2
$