156=n2

Solution for 156=n2 equation:

156=n2

We move all terms to the left:

156-(n2)=0

We add all the numbers together, and all the variables

-1n^2+156=0

a = -1; b = 0; c = +156;
Δ = b2-4ac
Δ = 02-4·(-1)·156
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*-1}=\frac{0-4\sqrt{39}}{-2}
=-\frac{4\sqrt{39}}{-2}
=-\frac{2\sqrt{39}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*-1}=\frac{0+4\sqrt{39}}{-2}
=\frac{4\sqrt{39}}{-2}
=\frac{2\sqrt{39}}{-1}
$