2x+12=12+2/3x

Solution for 2x+12=12+2/3x equation:

2x+12=12+2/3x

We move all terms to the left:

2x+12-(12+2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(2/3x+12)+12=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-2=0

a = 6; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·6·(-2)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*6}=\frac{0-4\sqrt{3}}{12}
=-\frac{4\sqrt{3}}{12}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*6}=\frac{0+4\sqrt{3}}{12}
=\frac{4\sqrt{3}}{12}
=\frac{\sqrt{3}}{3}
$