39=n2-3

Solution for 39=n2-3 equation:

39=n2-3

We move all terms to the left:

39-(n2-3)=0

We add all the numbers together, and all the variables

-(+n^2-3)+39=0

We get rid of parentheses

-n^2+3+39=0

We add all the numbers together, and all the variables

-1n^2+42=0

a = -1; b = 0; c = +42;
Δ = b2-4ac
Δ = 02-4·(-1)·42
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-1}=\frac{0-2\sqrt{42}}{-2}
=-\frac{2\sqrt{42}}{-2}
=-\frac{\sqrt{42}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-1}=\frac{0+2\sqrt{42}}{-2}
=\frac{2\sqrt{42}}{-2}
=\frac{\sqrt{42}}{-1}
$