5n+0.1594=8.4753642/n

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Solution for 5n+0.1594=8.4753642/n equation: 



5n+0.1594=8.4753642/n

We move all terms to the left:

5n+0.1594-(8.4753642/n)=0



Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R



We add all the numbers together, and all the variables

5n-(+8.4753642/n)+0.1594=0

We get rid of parentheses

5n-8.4753642/n+0.1594=0

We multiply all the terms by the denominator


5n*n+(0.1594)*n-8.4753642=0

We multiply parentheses

5n*n+0.1594n-8.4753642=0

Wy multiply elements

5n^2+0.1594n-8.4753642=0

a = 5; b = 0.1594; c = -8.4753642;
Δ = b2-4ac
Δ = 0.15942-4·5·(-8.4753642)
Δ = 169.53269236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.1594)-\sqrt{169.53269236}}{2*5}=\frac{-0.1594-\sqrt{169.53269236}}{10}
$


$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1594)+\sqrt{169.53269236}}{2*5}=\frac{-0.1594+\sqrt{169.53269236}}{10}
$

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