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

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

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

We move all terms to the left:

(X+6)-(2(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


X*3X+6*3X+6))-(2(1+6))=0

We add all the numbers together, and all the variables

X*3X+6*3X+6))-(27)=0

We add all the numbers together, and all the variables

X*3X+6*3X=0

Wy multiply elements

3X^2+18X=0

a = 3; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·3·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*3}=\frac{-36}{6}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*3}=\frac{0}{6}
=0
$