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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


1029x/1715x^2+20x/1715x^2+15x/1715x^2-1=0

We multiply all the terms by the denominator


1029x+20x+15x-1*1715x^2=0

We add all the numbers together, and all the variables

1064x-1*1715x^2=0

Wy multiply elements

-1715x^2+1064x=0

a = -1715; b = 1064; c = 0;
Δ = b2-4ac
Δ = 10642-4·(-1715)·0
Δ = 1132096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1132096}=1064$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1064)-1064}{2*-1715}=\frac{-2128}{-3430}
=152/245
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1064)+1064}{2*-1715}=\frac{0}{-3430}
=0
$