(1/3)n+4=7

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Solution for (1/3)n+4=7 equation:



(1/3)n+4=7
We move all terms to the left:
(1/3)n+4-(7)=0
Domain of the equation: 3)n!=0
n!=0/1
n!=0
n∈R
We add all the numbers together, and all the variables
(+1/3)n+4-7=0
We add all the numbers together, and all the variables
(+1/3)n-3=0
We multiply parentheses
n^2-3=0
a = 1; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1·(-3)
Δ = 12
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:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*1}=\frac{0-2\sqrt{3}}{2} =-\frac{2\sqrt{3}}{2} =-\sqrt{3} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*1}=\frac{0+2\sqrt{3}}{2} =\frac{2\sqrt{3}}{2} =\sqrt{3} $

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