5/3x-4/5=2/7x

Solution for 5/3x-4/5=2/7x equation:

5/3x-4/5=2/7x

We move all terms to the left:

5/3x-4/5-(2/7x)=0


Domain of the equation: 3x!=0

x!=0/3

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

5/3x-(+2/7x)-4/5=0

We get rid of parentheses

5/3x-2/7x-4/5=0

We calculate fractions


(-588x^2)/525x^2+875x/525x^2+(-150x)/525x^2=0

We multiply all the terms by the denominator


(-588x^2)+875x+(-150x)=0

We get rid of parentheses

-588x^2+875x-150x=0

We add all the numbers together, and all the variables

-588x^2+725x=0

a = -588; b = 725; c = 0;
Δ = b2-4ac
Δ = 7252-4·(-588)·0
Δ = 525625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{525625}=725$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(725)-725}{2*-588}=\frac{-1450}{-1176}
=1+137/588
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(725)+725}{2*-588}=\frac{0}{-1176}
=0
$