3/4n+16=21/8n

Solution for 3/4n+16=21/8n equation:

3/4n+16=21/8n

We move all terms to the left:

3/4n+16-(21/8n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(+21/8n)+16=0

We get rid of parentheses

3/4n-21/8n+16=0

We calculate fractions


24n/32n^2+(-84n)/32n^2+16=0

We multiply all the terms by the denominator


24n+(-84n)+16*32n^2=0

Wy multiply elements

512n^2+24n+(-84n)=0

We get rid of parentheses

512n^2+24n-84n=0

We add all the numbers together, and all the variables

512n^2-60n=0

a = 512; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·512·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*512}=\frac{0}{1024}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*512}=\frac{120}{1024}
=15/128
$