3/7x+1/3=1/3x+1

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

3/7x+1/3=1/3x+1

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


81x/189x^2+(-7x)/189x^2+7x/189x^2-1=0

We multiply all the terms by the denominator


81x+(-7x)+7x-1*189x^2=0

We add all the numbers together, and all the variables

88x+(-7x)-1*189x^2=0

Wy multiply elements

-189x^2+88x+(-7x)=0

We get rid of parentheses

-189x^2+88x-7x=0

We add all the numbers together, and all the variables

-189x^2+81x=0

a = -189; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-189)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-189}=\frac{-162}{-378}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-189}=\frac{0}{-378}
=0
$