2n+3/3n+5=2

Solution for 2n+3/3n+5=2 equation:

2n+3/3n+5=2

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

2n+3/3n+3=0

We multiply all the terms by the denominator


2n*3n+3*3n+3=0

Wy multiply elements

6n^2+9n+3=0

a = 6; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·6·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*6}=\frac{-12}{12}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*6}=\frac{-6}{12}
=-1/2
$