5/7x-1/5x=3

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

5/7x-1/5x=3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


25x/35x^2+(-7x)/35x^2-3=0

We multiply all the terms by the denominator


25x+(-7x)-3*35x^2=0

Wy multiply elements

-105x^2+25x+(-7x)=0

We get rid of parentheses

-105x^2+25x-7x=0

We add all the numbers together, and all the variables

-105x^2+18x=0

a = -105; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-105)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-105}=\frac{-36}{-210}
=6/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-105}=\frac{0}{-210}
=0
$