4/5+1/7x-1/3=6/5x

Solution for 4/5+1/7x-1/3=6/5x equation:

4/5+1/7x-1/3=6/5x

We move all terms to the left:

4/5+1/7x-1/3-(6/5x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(+6/5x)+4/5-1/3=0

We get rid of parentheses

1/7x-6/5x+4/5-1/3=0

We calculate fractions


(-875x^2)/2625x^2+375x/2625x^2+(-378x)/2625x^2+252x/2625x^2=0

We multiply all the terms by the denominator


(-875x^2)+375x+(-378x)+252x=0

We add all the numbers together, and all the variables

(-875x^2)+627x+(-378x)=0

We get rid of parentheses

-875x^2+627x-378x=0

We add all the numbers together, and all the variables

-875x^2+249x=0

a = -875; b = 249; c = 0;
Δ = b2-4ac
Δ = 2492-4·(-875)·0
Δ = 62001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62001}=249$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(249)-249}{2*-875}=\frac{-498}{-1750}
=249/875
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(249)+249}{2*-875}=\frac{0}{-1750}
=0
$