3/7x-(5/)=3

Solution for 3/7x-(5/)=3 equation:

3/7x-(5/)=3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3/7x-3-5/=0

We calculate fractions


()/(7x*)+(-35x)/(7x*)-3=0

We add all the numbers together, and all the variables

()/(+7x*)+(-35x)/(+7x*)-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

-21x^2-35x=0

a = -21; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-21)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-21}=\frac{70}{-42}
=-1+2/3
$