2n+2/3n=4

Solution for 2n+2/3n=4 equation:

2n+2/3n=4

We move all terms to the left:

2n+2/3n-(4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We multiply all the terms by the denominator


2n*3n-4*3n+2=0

Wy multiply elements

6n^2-12n+2=0

a = 6; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·6·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*6}=\frac{12-4\sqrt{6}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*6}=\frac{12+4\sqrt{6}}{12}
$