2-1/2n=1/4n+14

Solution for 2-1/2n=1/4n+14 equation:

2-1/2n=1/4n+14

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n+14)!=0

n∈R


We get rid of parentheses

-1/2n-1/4n-14+2=0

We calculate fractions


(-4n)/8n^2+(-2n)/8n^2-14+2=0

We add all the numbers together, and all the variables

(-4n)/8n^2+(-2n)/8n^2-12=0

We multiply all the terms by the denominator


(-4n)+(-2n)-12*8n^2=0

Wy multiply elements

-96n^2+(-4n)+(-2n)=0

We get rid of parentheses

-96n^2-4n-2n=0

We add all the numbers together, and all the variables

-96n^2-6n=0

a = -96; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-96)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-96}=\frac{0}{-192}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-96}=\frac{12}{-192}
=-1/16
$