1/3x+2=5/2x-4

Solution for 1/3x+2=5/2x-4 equation:

1/3x+2=5/2x-4

We move all terms to the left:

1/3x+2-(5/2x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

1/3x-5/2x+4+2=0

We calculate fractions


2x/6x^2+(-15x)/6x^2+4+2=0

We add all the numbers together, and all the variables

2x/6x^2+(-15x)/6x^2+6=0

We multiply all the terms by the denominator


2x+(-15x)+6*6x^2=0

Wy multiply elements

36x^2+2x+(-15x)=0

We get rid of parentheses

36x^2+2x-15x=0

We add all the numbers together, and all the variables

36x^2-13x=0

a = 36; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·36·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*36}=\frac{26}{72}
=13/36
$