1/2n+3=-1/8n-2

Solution for 1/2n+3=-1/8n-2 equation:

1/2n+3=-1/8n-2

We move all terms to the left:

1/2n+3-(-1/8n-2)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 8n-2)!=0

n∈R


We get rid of parentheses

1/2n+1/8n+2+3=0

We calculate fractions


8n/16n^2+2n/16n^2+2+3=0

We add all the numbers together, and all the variables

8n/16n^2+2n/16n^2+5=0

We multiply all the terms by the denominator


8n+2n+5*16n^2=0

We add all the numbers together, and all the variables

10n+5*16n^2=0

Wy multiply elements

80n^2+10n=0

a = 80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·80·0
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*80}=\frac{-20}{160}
=-1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*80}=\frac{0}{160}
=0
$