2/5x=1+2/7x

Solution for 2/5x=1+2/7x equation:

2/5x=1+2/7x

We move all terms to the left:

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

We get rid of parentheses

2/5x-2/7x-1=0

We calculate fractions


14x/35x^2+(-10x)/35x^2-1=0

We multiply all the terms by the denominator


14x+(-10x)-1*35x^2=0

Wy multiply elements

-35x^2+14x+(-10x)=0

We get rid of parentheses

-35x^2+14x-10x=0

We add all the numbers together, and all the variables

-35x^2+4x=0

a = -35; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-35)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-35}=\frac{-8}{-70}
=4/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-35}=\frac{0}{-70}
=0
$