2/3x+4=47+3/2x

Solution for 2/3x+4=47+3/2x equation:

2/3x+4=47+3/2x

We move all terms to the left:

2/3x+4-(47+3/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(3/2x+47)+4=0

We get rid of parentheses

2/3x-3/2x-47+4=0

We calculate fractions


4x/6x^2+(-9x)/6x^2-47+4=0

We add all the numbers together, and all the variables

4x/6x^2+(-9x)/6x^2-43=0

We multiply all the terms by the denominator


4x+(-9x)-43*6x^2=0

Wy multiply elements

-258x^2+4x+(-9x)=0

We get rid of parentheses

-258x^2+4x-9x=0

We add all the numbers together, and all the variables

-258x^2-5x=0

a = -258; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-258)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-258}=\frac{0}{-516}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-258}=\frac{10}{-516}
=-5/258
$