4n+3=9/2n

Solution for 4n+3=9/2n equation:

4n+3=9/2n

We move all terms to the left:

4n+3-(9/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

4n-(+9/2n)+3=0

We get rid of parentheses

4n-9/2n+3=0

We multiply all the terms by the denominator


4n*2n+3*2n-9=0

Wy multiply elements

8n^2+6n-9=0

a = 8; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·8·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*8}=\frac{-24}{16}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*8}=\frac{12}{16}
=3/4
$