1/2n+3=1/4n+5

Solution for 1/2n+3=1/4n+5 equation:

1/2n+3=1/4n+5

We move all terms to the left:

1/2n+3-(1/4n+5)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n+5)!=0

n∈R


We get rid of parentheses

1/2n-1/4n-5+3=0

We calculate fractions


4n/8n^2+(-2n)/8n^2-5+3=0

We add all the numbers together, and all the variables

4n/8n^2+(-2n)/8n^2-2=0

We multiply all the terms by the denominator


4n+(-2n)-2*8n^2=0

Wy multiply elements

-16n^2+4n+(-2n)=0

We get rid of parentheses

-16n^2+4n-2n=0

We add all the numbers together, and all the variables

-16n^2+2n=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$