2x+6=(1/3)(6x+9)

Solution for 2x+6=(1/3)(6x+9) equation:

2x+6=(1/3)(6x+9)

We move all terms to the left:

2x+6-((1/3)(6x+9))=0


Domain of the equation: 3)(6x+9))!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/3)(6x+9))+6=0

We multiply parentheses ..

-((+6x^2+1/3*9))+2x+6=0

We multiply all the terms by the denominator


-((+6x^2+1+2x*3*9))+6*3*9))=0


We calculate terms in parentheses: -((+6x^2+1+2x*3*9)), so:

(+6x^2+1+2x*3*9)

We get rid of parentheses

6x^2+2x*3*9+1

Wy multiply elements

6x^2+54x*9+1

Wy multiply elements

6x^2+486x+1

Back to the equation:

-(6x^2+486x+1)


We add all the numbers together, and all the variables

-(6x^2+486x+1)=0

We get rid of parentheses

-6x^2-486x-1=0

a = -6; b = -486; c = -1;
Δ = b2-4ac
Δ = -4862-4·(-6)·(-1)
Δ = 236172
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:

$\sqrt{\Delta}=\sqrt{236172}=\sqrt{4*59043}=\sqrt{4}*\sqrt{59043}=2\sqrt{59043}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-486)-2\sqrt{59043}}{2*-6}=\frac{486-2\sqrt{59043}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-486)+2\sqrt{59043}}{2*-6}=\frac{486+2\sqrt{59043}}{-12}
$