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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


36x^2/150x^2+225x/150x^2+(-100x)/150x^2+1+1=0

We add all the numbers together, and all the variables

36x^2/150x^2+225x/150x^2+(-100x)/150x^2+2=0

We multiply all the terms by the denominator


36x^2+225x+(-100x)+2*150x^2=0

Wy multiply elements

36x^2+300x^2+225x+(-100x)=0

We get rid of parentheses

36x^2+300x^2+225x-100x=0

We add all the numbers together, and all the variables

336x^2+125x=0

a = 336; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·336·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*336}=\frac{-250}{672}
=-125/336
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*336}=\frac{0}{672}
=0
$