182/n=13n

Solution for 182/n=13n equation:

182/n=13n

We move all terms to the left:

182/n-(13n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-13n+182/n=0

We multiply all the terms by the denominator


-13n*n+182=0

Wy multiply elements

-13n^2+182=0

a = -13; b = 0; c = +182;
Δ = b2-4ac
Δ = 02-4·(-13)·182
Δ = 9464
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:

$\sqrt{\Delta}=\sqrt{9464}=\sqrt{676*14}=\sqrt{676}*\sqrt{14}=26\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{14}}{2*-13}=\frac{0-26\sqrt{14}}{-26}
=-\frac{26\sqrt{14}}{-26}
=-\frac{\sqrt{14}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{14}}{2*-13}=\frac{0+26\sqrt{14}}{-26}
=\frac{26\sqrt{14}}{-26}
=\frac{\sqrt{14}}{-1}
$