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(12/100)n=78
We move all terms to the left:
(12/100)n-(78)=0
Domain of the equation: 100)n!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
(+12/100)n-78=0
We multiply parentheses
12n^2-78=0
a = 12; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·12·(-78)
Δ = 3744
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*12}=\frac{0-12\sqrt{26}}{24} =-\frac{12\sqrt{26}}{24} =-\frac{\sqrt{26}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*12}=\frac{0+12\sqrt{26}}{24} =\frac{12\sqrt{26}}{24} =\frac{\sqrt{26}}{2} $
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