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

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

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

We move all terms to the left:

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


Domain of the equation: 5.x!=0

x!=0/5.

x!=0

x∈R



Domain of the equation: 3.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


15x^2/(5.x*3.x*2)+18x/(5.x*3.x*2)+(-20x)/(5.x*3.x*2)=0

We add all the numbers together, and all the variables

15x^2/(+5.x*3.x*2)+18x/(+5.x*3.x*2)+(-20x)/(+5.x*3.x*2)=0

We multiply all the terms by the denominator


15x^2+18x+(-20x)=0

We get rid of parentheses

15x^2+18x-20x=0

We add all the numbers together, and all the variables

15x^2-2x=0

a = 15; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·15·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*15}=\frac{4}{30}
=2/15
$