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1/2n+45=172n=
We move all terms to the left:
1/2n+45-(172n)=0
Domain of the equation: 2n!=0We add all the numbers together, and all the variables
n!=0/2
n!=0
n∈R
-172n+1/2n+45=0
We multiply all the terms by the denominator
-172n*2n+45*2n+1=0
Wy multiply elements
-344n^2+90n+1=0
a = -344; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-344)·1
Δ = 9476
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9476}=\sqrt{4*2369}=\sqrt{4}*\sqrt{2369}=2\sqrt{2369}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2369}}{2*-344}=\frac{-90-2\sqrt{2369}}{-688} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2369}}{2*-344}=\frac{-90+2\sqrt{2369}}{-688} $
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