5n+1/2n=4

Solution for 5n+1/2n=4 equation:

5n+1/2n=4

We move all terms to the left:

5n+1/2n-(4)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


5n*2n-4*2n+1=0

Wy multiply elements

10n^2-8n+1=0

a = 10; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·10·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*10}=\frac{8-2\sqrt{6}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*10}=\frac{8+2\sqrt{6}}{20}
$