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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


375x/250x^2+14x/250x^2+(-14x)/250x^2+4=0

We multiply all the terms by the denominator


375x+14x+(-14x)+4*250x^2=0

We add all the numbers together, and all the variables

389x+(-14x)+4*250x^2=0

Wy multiply elements

1000x^2+389x+(-14x)=0

We get rid of parentheses

1000x^2+389x-14x=0

We add all the numbers together, and all the variables

1000x^2+375x=0

a = 1000; b = 375; c = 0;
Δ = b2-4ac
Δ = 3752-4·1000·0
Δ = 140625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{140625}=375$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(375)-375}{2*1000}=\frac{-750}{2000}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(375)+375}{2*1000}=\frac{0}{2000}
=0
$