3n+4=27/2n

Solution for 3n+4=27/2n equation:

3n+4=27/2n

We move all terms to the left:

3n+4-(27/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3n-(+27/2n)+4=0

We get rid of parentheses

3n-27/2n+4=0

We multiply all the terms by the denominator


3n*2n+4*2n-27=0

Wy multiply elements

6n^2+8n-27=0

a = 6; b = 8; c = -27;
Δ = b2-4ac
Δ = 82-4·6·(-27)
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{178}}{2*6}=\frac{-8-2\sqrt{178}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{178}}{2*6}=\frac{-8+2\sqrt{178}}{12}
$