2/5x-3/7=1-4/7x

Solution for 2/5x-3/7=1-4/7x equation:

2/5x-3/7=1-4/7x

We move all terms to the left:

2/5x-3/7-(1-4/7x)=0


Domain of the equation: 5x!=0

x!=0/5

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

2/5x-(-4/7x+1)-3/7=0

We get rid of parentheses

2/5x+4/7x-1-3/7=0

We calculate fractions


686x/1715x^2+20x/1715x^2+(-15x)/1715x^2-1=0

We multiply all the terms by the denominator


686x+20x+(-15x)-1*1715x^2=0

We add all the numbers together, and all the variables

706x+(-15x)-1*1715x^2=0

Wy multiply elements

-1715x^2+706x+(-15x)=0

We get rid of parentheses

-1715x^2+706x-15x=0

We add all the numbers together, and all the variables

-1715x^2+691x=0

a = -1715; b = 691; c = 0;
Δ = b2-4ac
Δ = 6912-4·(-1715)·0
Δ = 477481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{477481}=691$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(691)-691}{2*-1715}=\frac{-1382}{-3430}
=691/1715
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(691)+691}{2*-1715}=\frac{0}{-3430}
=0
$