364/n=26n=

Solution for 364/n=26n= equation:

364/n=26n=

We move all terms to the left:

364/n-(26n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-26n+364/n=0

We multiply all the terms by the denominator


-26n*n+364=0

Wy multiply elements

-26n^2+364=0

a = -26; b = 0; c = +364;
Δ = b2-4ac
Δ = 02-4·(-26)·364
Δ = 37856
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:

$\sqrt{\Delta}=\sqrt{37856}=\sqrt{2704*14}=\sqrt{2704}*\sqrt{14}=52\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{14}}{2*-26}=\frac{0-52\sqrt{14}}{-52}
=-\frac{52\sqrt{14}}{-52}
=-\frac{\sqrt{14}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{14}}{2*-26}=\frac{0+52\sqrt{14}}{-52}
=\frac{52\sqrt{14}}{-52}
=\frac{\sqrt{14}}{-1}
$