(11/4)n=36

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Solution for (11/4)n=36 equation:



(11/4)n=36
We move all terms to the left:
(11/4)n-(36)=0
Domain of the equation: 4)n!=0
n!=0/1
n!=0
n∈R
We add all the numbers together, and all the variables
(+11/4)n-36=0
We multiply parentheses
11n^2-36=0
a = 11; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·11·(-36)
Δ = 1584
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:
$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*11}=\frac{0-12\sqrt{11}}{22} =-\frac{12\sqrt{11}}{22} =-\frac{6\sqrt{11}}{11} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*11}=\frac{0+12\sqrt{11}}{22} =\frac{12\sqrt{11}}{22} =\frac{6\sqrt{11}}{11} $

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