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

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

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

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: n+16)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


(-n)/2n^2+(-6n)/2n^2-16+2=0

We add all the numbers together, and all the variables

(-1n)/2n^2+(-6n)/2n^2-16+2=0

We add all the numbers together, and all the variables

(-1n)/2n^2+(-6n)/2n^2-14=0

We multiply all the terms by the denominator


(-1n)+(-6n)-14*2n^2=0

Wy multiply elements

-28n^2+(-1n)+(-6n)=0

We get rid of parentheses

-28n^2-1n-6n=0

We add all the numbers together, and all the variables

-28n^2-7n=0

a = -28; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-28)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-28}=\frac{0}{-56}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-28}=\frac{14}{-56}
=-1/4
$