5/3+3/2x=2+2/3x

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

5/3+3/2x=2+2/3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


81x/54x^2+(-4x)/54x^2+10x/54x^2-2=0

We multiply all the terms by the denominator


81x+(-4x)+10x-2*54x^2=0

We add all the numbers together, and all the variables

91x+(-4x)-2*54x^2=0

Wy multiply elements

-108x^2+91x+(-4x)=0

We get rid of parentheses

-108x^2+91x-4x=0

We add all the numbers together, and all the variables

-108x^2+87x=0

a = -108; b = 87; c = 0;
Δ = b2-4ac
Δ = 872-4·(-108)·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-87}{2*-108}=\frac{-174}{-216}
=29/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+87}{2*-108}=\frac{0}{-216}
=0
$