n(4n-1)-5=0

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Solution for n(4n-1)-5=0 equation:



n(4n-1)-5=0
We multiply parentheses
4n^2-1n-5=0
a = 4; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·4·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*4}=\frac{-8}{8} =-1 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*4}=\frac{10}{8} =1+1/4 $

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