3/7x-5/1x=3

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

3/7x-5/1x=3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 1x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-21x^2+3x+(-35x)=0

We get rid of parentheses

-21x^2+3x-35x=0

We add all the numbers together, and all the variables

-21x^2-32x=0

a = -21; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-21)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-21}=\frac{64}{-42}
=-1+11/21
$