1/2n-9=1+-1/8n

Solution for 1/2n-9=1+-1/8n equation:

1/2n-9=1+-1/8n

We move all terms to the left:

1/2n-9-(1+-1/8n)=0


Domain of the equation: 2n!=0

n!=0/2

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

1/2n-(-1/8n)-9=0

We get rid of parentheses

1/2n+1/8n-9=0

We calculate fractions


8n/16n^2+2n/16n^2-9=0

We multiply all the terms by the denominator


8n+2n-9*16n^2=0

We add all the numbers together, and all the variables

10n-9*16n^2=0

Wy multiply elements

-144n^2+10n=0

a = -144; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-144)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-144}=\frac{-20}{-288}
=5/72
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-144}=\frac{0}{-288}
=0
$