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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


63x^2/525x^2+225x/525x^2+(-350x)/525x^2+1=0

We multiply all the terms by the denominator


63x^2+225x+(-350x)+1*525x^2=0

Wy multiply elements

63x^2+525x^2+225x+(-350x)=0

We get rid of parentheses

63x^2+525x^2+225x-350x=0

We add all the numbers together, and all the variables

588x^2-125x=0

a = 588; b = -125; c = 0;
Δ = b2-4ac
Δ = -1252-4·588·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-125}{2*588}=\frac{0}{1176}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+125}{2*588}=\frac{250}{1176}
=125/588
$