4/7x-2/3=3-1/3x

Solution for 4/7x-2/3=3-1/3x equation:

4/7x-2/3=3-1/3x

We move all terms to the left:

4/7x-2/3-(3-1/3x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/7x-(-1/3x+3)-2/3=0

We get rid of parentheses

4/7x+1/3x-3-2/3=0

We calculate fractions


108x/189x^2+7x/189x^2+(-14x)/189x^2-3=0

We multiply all the terms by the denominator


108x+7x+(-14x)-3*189x^2=0

We add all the numbers together, and all the variables

115x+(-14x)-3*189x^2=0

Wy multiply elements

-567x^2+115x+(-14x)=0

We get rid of parentheses

-567x^2+115x-14x=0

We add all the numbers together, and all the variables

-567x^2+101x=0

a = -567; b = 101; c = 0;
Δ = b2-4ac
Δ = 1012-4·(-567)·0
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-101}{2*-567}=\frac{-202}{-1134}
=101/567
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+101}{2*-567}=\frac{0}{-1134}
=0
$