(n^2)+1=1522

Solution for (n^2)+1=1522 equation:

(n^2)+1=1522

We move all terms to the left:

(n^2)+1-(1522)=0

We add all the numbers together, and all the variables

n^2-1521=0

a = 1; b = 0; c = -1521;
Δ = b2-4ac
Δ = 02-4·1·(-1521)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-78}{2*1}=\frac{-78}{2}
=-39
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+78}{2*1}=\frac{78}{2}
=39
$