n^2+16n+63=1000

Solution for n^2+16n+63=1000 equation:

n^2+16n+63=1000

We move all terms to the left:

n^2+16n+63-(1000)=0

We add all the numbers together, and all the variables

n^2+16n-937=0

a = 1; b = 16; c = -937;
Δ = b2-4ac
Δ = 162-4·1·(-937)
Δ = 4004
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:

$\sqrt{\Delta}=\sqrt{4004}=\sqrt{4*1001}=\sqrt{4}*\sqrt{1001}=2\sqrt{1001}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{1001}}{2*1}=\frac{-16-2\sqrt{1001}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{1001}}{2*1}=\frac{-16+2\sqrt{1001}}{2}
$