n2=25/26

Solution for n2=25/26 equation:

n2=25/26

We move all terms to the left:

n2-(25/26)=0

We add all the numbers together, and all the variables

n2-(+25/26)=0

We add all the numbers together, and all the variables

n^2-(+25/26)=0

We get rid of parentheses

n^2-25/26=0

We multiply all the terms by the denominator


n^2*26-25=0

Wy multiply elements

26n^2-25=0

a = 26; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·26·(-25)
Δ = 2600
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:

$\sqrt{\Delta}=\sqrt{2600}=\sqrt{100*26}=\sqrt{100}*\sqrt{26}=10\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{26}}{2*26}=\frac{0-10\sqrt{26}}{52}
=-\frac{10\sqrt{26}}{52}
=-\frac{5\sqrt{26}}{26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{26}}{2*26}=\frac{0+10\sqrt{26}}{52}
=\frac{10\sqrt{26}}{52}
=\frac{5\sqrt{26}}{26}
$