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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-x*3x-4*3x+4*3x+3=0

Wy multiply elements

-3x^2-12x+12x+3=0

We add all the numbers together, and all the variables

-3x^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$