2/2x+4=5/3x-2

Solution for 2/2x+4=5/3x-2 equation:

2/2x+4=5/3x-2

We move all terms to the left:

2/2x+4-(5/3x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

2/2x-5/3x+2+4=0

We calculate fractions


6x/6x^2+(-10x)/6x^2+2+4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

36x^2+6x+(-10x)=0

We get rid of parentheses

36x^2+6x-10x=0

We add all the numbers together, and all the variables

36x^2-4x=0

a = 36; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·36·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*36}=\frac{8}{72}
=1/9
$