2n+6=2/5n

Solution for 2n+6=2/5n equation:

2n+6=2/5n

We move all terms to the left:

2n+6-(2/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2n-(+2/5n)+6=0

We get rid of parentheses

2n-2/5n+6=0

We multiply all the terms by the denominator


2n*5n+6*5n-2=0

Wy multiply elements

10n^2+30n-2=0

a = 10; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·10·(-2)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14\sqrt{5}}{2*10}=\frac{-30-14\sqrt{5}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14\sqrt{5}}{2*10}=\frac{-30+14\sqrt{5}}{20}
$