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

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

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

We move all terms to the left:

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


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-4n)/32n^2+(-24n)/32n^2-14=0

We multiply all the terms by the denominator


(-4n)+(-24n)-14*32n^2=0

Wy multiply elements

-448n^2+(-4n)+(-24n)=0

We get rid of parentheses

-448n^2-4n-24n=0

We add all the numbers together, and all the variables

-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{0}{-896}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-448}=\frac{56}{-896}
=-1/16
$