-2=-2n+2/3n

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

-2=-2n+2/3n

We move all terms to the left:

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


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

2n-2/3n-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

6n^2-6n-2=0

a = 6; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·6·(-2)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*6}=\frac{6-2\sqrt{21}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*6}=\frac{6+2\sqrt{21}}{12}
$