(3/2)n-6=22

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Solution for (3/2)n-6=22 equation:



(3/2)n-6=22
We move all terms to the left:
(3/2)n-6-(22)=0
Domain of the equation: 2)n!=0
n!=0/1
n!=0
n∈R
We add all the numbers together, and all the variables
(+3/2)n-6-22=0
We add all the numbers together, and all the variables
(+3/2)n-28=0
We multiply parentheses
3n^2-28=0
a = 3; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·3·(-28)
Δ = 336
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:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*3}=\frac{0-4\sqrt{21}}{6} =-\frac{4\sqrt{21}}{6} =-\frac{2\sqrt{21}}{3} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*3}=\frac{0+4\sqrt{21}}{6} =\frac{4\sqrt{21}}{6} =\frac{2\sqrt{21}}{3} $

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