-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+14=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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