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

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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} $

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