1/3x+2=3-2/7x

Solution for 1/3x+2=3-2/7x equation:

1/3x+2=3-2/7x

We move all terms to the left:

1/3x+2-(3-2/7x)=0


Domain of the equation: 3x!=0

x!=0/3

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

1/3x-(-2/7x+3)+2=0

We get rid of parentheses

1/3x+2/7x-3+2=0

We calculate fractions


7x/21x^2+6x/21x^2-3+2=0

We add all the numbers together, and all the variables

7x/21x^2+6x/21x^2-1=0

We multiply all the terms by the denominator


7x+6x-1*21x^2=0

We add all the numbers together, and all the variables

13x-1*21x^2=0

Wy multiply elements

-21x^2+13x=0

a = -21; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-21)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-21}=\frac{-26}{-42}
=13/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-21}=\frac{0}{-42}
=0
$