2n+1/2*n=10

Solution for 2n+1/2*n=10 equation:

2n+1/2n=10

We move all terms to the left:

2n+1/2n-(10)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


2n*2n-10*2n+1=0

Wy multiply elements

4n^2-20n+1=0

a = 4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*4}=\frac{20-8\sqrt{6}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*4}=\frac{20+8\sqrt{6}}{8}
$