2/x+3=20/7x

Solution for 2/x+3=20/7x equation:

2/x+3=20/7x

We move all terms to the left:

2/x+3-(20/7x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(+20/7x)+3=0

We get rid of parentheses

2/x-20/7x+3=0

We calculate fractions


14x/7x^2+(-20x)/7x^2+3=0

We multiply all the terms by the denominator


14x+(-20x)+3*7x^2=0

Wy multiply elements

21x^2+14x+(-20x)=0

We get rid of parentheses

21x^2+14x-20x=0

We add all the numbers together, and all the variables

21x^2-6x=0

a = 21; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·21·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*21}=\frac{0}{42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*21}=\frac{12}{42}
=2/7
$