2/3n+2=3n

Solution for 2/3n+2=3n equation:

2/3n+2=3n

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-3n+2/3n+2=0

We multiply all the terms by the denominator


-3n*3n+2*3n+2=0

Wy multiply elements

-9n^2+6n+2=0

a = -9; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-9)·2
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-9}=\frac{-6-6\sqrt{3}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-9}=\frac{-6+6\sqrt{3}}{-18}
$