8+2n+2=20-3/2n

Solution for 8+2n+2=20-3/2n equation:

8+2n+2=20-3/2n

We move all terms to the left:

8+2n+2-(20-3/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2n-(-3/2n+20)+8+2=0

We add all the numbers together, and all the variables

2n-(-3/2n+20)+10=0

We get rid of parentheses

2n+3/2n-20+10=0

We multiply all the terms by the denominator


2n*2n-20*2n+10*2n+3=0

Wy multiply elements

4n^2-40n+20n+3=0

We add all the numbers together, and all the variables

4n^2-20n+3=0

a = 4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·4·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{22}}{2*4}=\frac{20-4\sqrt{22}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{22}}{2*4}=\frac{20+4\sqrt{22}}{8}
$