4/5x+3=2/7x-1

Solution for 4/5x+3=2/7x-1 equation:

4/5x+3=2/7x-1

We move all terms to the left:

4/5x+3-(2/7x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x-1)!=0

x∈R


We get rid of parentheses

4/5x-2/7x+1+3=0

We calculate fractions


28x/35x^2+(-10x)/35x^2+1+3=0

We add all the numbers together, and all the variables

28x/35x^2+(-10x)/35x^2+4=0

We multiply all the terms by the denominator


28x+(-10x)+4*35x^2=0

Wy multiply elements

140x^2+28x+(-10x)=0

We get rid of parentheses

140x^2+28x-10x=0

We add all the numbers together, and all the variables

140x^2+18x=0

a = 140; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·140·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*140}=\frac{-36}{280}
=-9/70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*140}=\frac{0}{280}
=0
$