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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


686x/1029x^2+12x/1029x^2+9x/1029x^2-1=0

We multiply all the terms by the denominator


686x+12x+9x-1*1029x^2=0

We add all the numbers together, and all the variables

707x-1*1029x^2=0

Wy multiply elements

-1029x^2+707x=0

a = -1029; b = 707; c = 0;
Δ = b2-4ac
Δ = 7072-4·(-1029)·0
Δ = 499849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{499849}=707$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(707)-707}{2*-1029}=\frac{-1414}{-2058}
=101/147
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(707)+707}{2*-1029}=\frac{0}{-2058}
=0
$