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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/10x^2+(-15x)/10x^2+4+2=0

We add all the numbers together, and all the variables

6x/10x^2+(-15x)/10x^2+6=0

We multiply all the terms by the denominator


6x+(-15x)+6*10x^2=0

Wy multiply elements

60x^2+6x+(-15x)=0

We get rid of parentheses

60x^2+6x-15x=0

We add all the numbers together, and all the variables

60x^2-9x=0

a = 60; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·60·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*60}=\frac{18}{120}
=3/20
$