9+31/2n=11-4/8n

Solution for 9+31/2n=11-4/8n equation:

9+31/2n=11-4/8n

We move all terms to the left:

9+31/2n-(11-4/8n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

31/2n-(-4/8n+11)+9=0

We get rid of parentheses

31/2n+4/8n-11+9=0

We calculate fractions


248n/16n^2+8n/16n^2-11+9=0

We add all the numbers together, and all the variables

248n/16n^2+8n/16n^2-2=0

We multiply all the terms by the denominator


248n+8n-2*16n^2=0

We add all the numbers together, and all the variables

256n-2*16n^2=0

Wy multiply elements

-32n^2+256n=0

a = -32; b = 256; c = 0;
Δ = b2-4ac
Δ = 2562-4·(-32)·0
Δ = 65536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65536}=256$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-256}{2*-32}=\frac{-512}{-64}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+256}{2*-32}=\frac{0}{-64}
=0
$