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

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

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

We move all terms to the left:

3/4(n)+16-(2-1/8(n))=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+14=0

We multiply all the terms by the denominator


24n+4n+14*32n^2=0

We add all the numbers together, and all the variables

28n+14*32n^2=0

Wy multiply elements

448n^2+28n=0

a = 448; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·448·0
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*448}=\frac{-56}{896}
=-1/16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*448}=\frac{0}{896}
=0
$