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7/2*n=1
We move all terms to the left:
7/2*n-(1)=0
Domain of the equation: 2*n!=0We multiply all the terms by the denominator
n!=0/1
n!=0
n∈R
-1*2*n+7=0
Wy multiply elements
-2n*n+7=0
Wy multiply elements
-2n^2+7=0
a = -2; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2)·7
Δ = 56
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-2}=\frac{0-2\sqrt{14}}{-4} =-\frac{2\sqrt{14}}{-4} =-\frac{\sqrt{14}}{-2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-2}=\frac{0+2\sqrt{14}}{-4} =\frac{2\sqrt{14}}{-4} =\frac{\sqrt{14}}{-2} $
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