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81n^2+5=14
We move all terms to the left:
81n^2+5-(14)=0
We add all the numbers together, and all the variables
81n^2-9=0
a = 81; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·81·(-9)
Δ = 2916
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2916}=54$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*81}=\frac{-54}{162} =-1/3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*81}=\frac{54}{162} =1/3 $
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