3/4n+4=-1/2n-1

Solution for 3/4n+4=-1/2n-1 equation:

3/4n+4=-1/2n-1

We move all terms to the left:

3/4n+4-(-1/2n-1)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n-1)!=0

n∈R


We get rid of parentheses

3/4n+1/2n+1+4=0

We calculate fractions


6n/8n^2+4n/8n^2+1+4=0

We add all the numbers together, and all the variables

6n/8n^2+4n/8n^2+5=0

We multiply all the terms by the denominator


6n+4n+5*8n^2=0

We add all the numbers together, and all the variables

10n+5*8n^2=0

Wy multiply elements

40n^2+10n=0

a = 40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·40·0
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*40}=\frac{-20}{80}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*40}=\frac{0}{80}
=0
$