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

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

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

We move all terms to the left:

1/2x+1/3-(4+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

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

We get rid of parentheses

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

We calculate fractions


27x/54x^2+(-4x)/54x^2+2x/54x^2-4=0

We multiply all the terms by the denominator


27x+(-4x)+2x-4*54x^2=0

We add all the numbers together, and all the variables

29x+(-4x)-4*54x^2=0

Wy multiply elements

-216x^2+29x+(-4x)=0

We get rid of parentheses

-216x^2+29x-4x=0

We add all the numbers together, and all the variables

-216x^2+25x=0

a = -216; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-216)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-216}=\frac{-50}{-432}
=25/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-216}=\frac{0}{-432}
=0
$