5/2n-1n=3+3/2n

Solution for 5/2n-1n=3+3/2n equation:

5/2n-1n=3+3/2n

We move all terms to the left:

5/2n-1n-(3+3/2n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5/2n-1n-(3/2n+3)=0

We add all the numbers together, and all the variables

-1n+5/2n-(3/2n+3)=0

We get rid of parentheses

-1n+5/2n-3/2n-3=0

We multiply all the terms by the denominator


-1n*2n-3*2n+5-3=0

We add all the numbers together, and all the variables

-1n*2n-3*2n+2=0

Wy multiply elements

-2n^2-6n+2=0

a = -2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-2)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-2}=\frac{6-2\sqrt{13}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-2}=\frac{6+2\sqrt{13}}{-4}
$