3n+5=3/4n

Solution for 3n+5=3/4n equation:

3n+5=3/4n

We move all terms to the left:

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


Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3n-3/4n+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

12n^2+20n-3=0

a = 12; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·12·(-3)
Δ = 544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{34}}{2*12}=\frac{-20-4\sqrt{34}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{34}}{2*12}=\frac{-20+4\sqrt{34}}{24}
$