8n+5/2n=41

Solution for 8n+5/2n=41 equation:

8n+5/2n=41

We move all terms to the left:

8n+5/2n-(41)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


8n*2n-41*2n+5=0

Wy multiply elements

16n^2-82n+5=0

a = 16; b = -82; c = +5;
Δ = b2-4ac
Δ = -822-4·16·5
Δ = 6404
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:

$\sqrt{\Delta}=\sqrt{6404}=\sqrt{4*1601}=\sqrt{4}*\sqrt{1601}=2\sqrt{1601}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1601}}{2*16}=\frac{82-2\sqrt{1601}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1601}}{2*16}=\frac{82+2\sqrt{1601}}{32}
$