59=n2

Solution for 59=n2 equation:

59=n2

We move all terms to the left:

59-(n2)=0

We add all the numbers together, and all the variables

-1n^2+59=0

a = -1; b = 0; c = +59;
Δ = b2-4ac
Δ = 02-4·(-1)·59
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{59}}{2*-1}=\frac{0-2\sqrt{59}}{-2}
=-\frac{2\sqrt{59}}{-2}
=-\frac{\sqrt{59}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{59}}{2*-1}=\frac{0+2\sqrt{59}}{-2}
=\frac{2\sqrt{59}}{-2}
=\frac{\sqrt{59}}{-1}
$