6=n2-20

Solution for 6=n2-20 equation:

6=n2-20

We move all terms to the left:

6-(n2-20)=0

We add all the numbers together, and all the variables

-(+n^2-20)+6=0

We get rid of parentheses

-n^2+20+6=0

We add all the numbers together, and all the variables

-1n^2+26=0

a = -1; b = 0; c = +26;
Δ = b2-4ac
Δ = 02-4·(-1)·26
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-1}=\frac{0-2\sqrt{26}}{-2}
=-\frac{2\sqrt{26}}{-2}
=-\frac{\sqrt{26}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-1}=\frac{0+2\sqrt{26}}{-2}
=\frac{2\sqrt{26}}{-2}
=\frac{\sqrt{26}}{-1}
$