n*n+301-9930=0

Solution for n*n+301-9930=0 equation:

n*n+301-9930=0

We add all the numbers together, and all the variables

n*n-9629=0

Wy multiply elements

n^2-9629=0

a = 1; b = 0; c = -9629;
Δ = b2-4ac
Δ = 02-4·1·(-9629)
Δ = 38516
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:

$\sqrt{\Delta}=\sqrt{38516}=\sqrt{4*9629}=\sqrt{4}*\sqrt{9629}=2\sqrt{9629}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{9629}}{2*1}=\frac{0-2\sqrt{9629}}{2}
=-\frac{2\sqrt{9629}}{2}
=-\sqrt{9629}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{9629}}{2*1}=\frac{0+2\sqrt{9629}}{2}
=\frac{2\sqrt{9629}}{2}
=\sqrt{9629}
$