5n-4n=2/3n+2

Solution for 5n-4n=2/3n+2 equation:

5n-4n=2/3n+2

We move all terms to the left:

5n-4n-(2/3n+2)=0


Domain of the equation: 3n+2)!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

n-2/3n-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3n^2-6n-2=0

a = 3; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·3·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*3}=\frac{6-2\sqrt{15}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*3}=\frac{6+2\sqrt{15}}{6}
$