2(x+6)=3(6+1/3x)

Solution for 2(x+6)=3(6+1/3x) equation:

2(x+6)=3(6+1/3x)

We move all terms to the left:

2(x+6)-(3(6+1/3x))=0


Domain of the equation: 3x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(x+6)-(3(1/3x+6))=0

We multiply parentheses

2x-(3(1/3x+6))+12=0

We multiply all the terms by the denominator


2x*3x+12*3x+6))-(3(1+6))=0

We add all the numbers together, and all the variables

2x*3x+12*3x+6))-(37)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2+36x=0

a = 6; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*6}=\frac{0}{12}
=0
$