5/3x=3/2x-1

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

5/3x=3/2x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/6x^2+(-9x)/6x^2+1=0

We multiply all the terms by the denominator


10x+(-9x)+1*6x^2=0

Wy multiply elements

6x^2+10x+(-9x)=0

We get rid of parentheses

6x^2+10x-9x=0

We add all the numbers together, and all the variables

6x^2+x=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12}
=0
$