3/4n-16=2-1/8n

Solution for 3/4n-16=2-1/8n equation:

3/4n-16=2-1/8n

We move all terms to the left:

3/4n-16-(2-1/8n)=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-(-1/8n+2)-16=0

We get rid of parentheses

3/4n+1/8n-2-16=0

We calculate fractions


24n/32n^2+4n/32n^2-2-16=0

We add all the numbers together, and all the variables

24n/32n^2+4n/32n^2-18=0

We multiply all the terms by the denominator


24n+4n-18*32n^2=0

We add all the numbers together, and all the variables

28n-18*32n^2=0

Wy multiply elements

-576n^2+28n=0

a = -576; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-576)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-576}=\frac{-56}{-1152}
=7/144
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-576}=\frac{0}{-1152}
=0
$