-3/4n+2n=-5-15/4n

Solution for -3/4n+2n=-5-15/4n equation:

-3/4n+2n=-5-15/4n

We move all terms to the left:

-3/4n+2n-(-5-15/4n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-3/4n+2n-(-15/4n-5)=0

We add all the numbers together, and all the variables

2n-3/4n-(-15/4n-5)=0

We get rid of parentheses

2n-3/4n+15/4n+5=0

We multiply all the terms by the denominator


2n*4n+5*4n-3+15=0

We add all the numbers together, and all the variables

2n*4n+5*4n+12=0

Wy multiply elements

8n^2+20n+12=0

a = 8; b = 20; c = +12;
Δ = b2-4ac
Δ = 202-4·8·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*8}=\frac{-24}{16}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*8}=\frac{-16}{16}
=-1
$