1/4n-9=-1/2n

Solution for 1/4n-9=-1/2n equation:

1/4n-9=-1/2n

We move all terms to the left:

1/4n-9-(-1/2n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

1/4n+1/2n-9=0

We calculate fractions


2n/8n^2+4n/8n^2-9=0

We multiply all the terms by the denominator


2n+4n-9*8n^2=0

We add all the numbers together, and all the variables

6n-9*8n^2=0

Wy multiply elements

-72n^2+6n=0

a = -72; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-72)·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*-72}=\frac{-12}{-144}
=1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-72}=\frac{0}{-144}
=0
$