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

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

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

We move all terms to the left:

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


Domain of the equation: 3n+6))!=0

n∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

n*3n+2*3n+6))-(37)=0

We add all the numbers together, and all the variables

n*3n+2*3n=0

Wy multiply elements

3n^2+6n=0

a = 3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*3}=\frac{-12}{6}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*3}=\frac{0}{6}
=0
$