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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


375x/250x^2+(-2x)/250x^2+(-6x)/250x^2+2=0

We multiply all the terms by the denominator


375x+(-2x)+(-6x)+2*250x^2=0

Wy multiply elements

500x^2+375x+(-2x)+(-6x)=0

We get rid of parentheses

500x^2+375x-2x-6x=0

We add all the numbers together, and all the variables

500x^2+367x=0

a = 500; b = 367; c = 0;
Δ = b2-4ac
Δ = 3672-4·500·0
Δ = 134689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{134689}=367$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(367)-367}{2*500}=\frac{-734}{1000}
=-367/500
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(367)+367}{2*500}=\frac{0}{1000}
=0
$