3n+5/2n=44

Solution for 3n+5/2n=44 equation:

3n+5/2n=44

We move all terms to the left:

3n+5/2n-(44)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


3n*2n-44*2n+5=0

Wy multiply elements

6n^2-88n+5=0

a = 6; b = -88; c = +5;
Δ = b2-4ac
Δ = -882-4·6·5
Δ = 7624
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:

$\sqrt{\Delta}=\sqrt{7624}=\sqrt{4*1906}=\sqrt{4}*\sqrt{1906}=2\sqrt{1906}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1906}}{2*6}=\frac{88-2\sqrt{1906}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1906}}{2*6}=\frac{88+2\sqrt{1906}}{12}
$