1000=8n+5n^2

Solution for 1000=8n+5n^2 equation:

1000=8n+5n^2

We move all terms to the left:

1000-(8n+5n^2)=0

We get rid of parentheses

-5n^2-8n+1000=0

a = -5; b = -8; c = +1000;
Δ = b2-4ac
Δ = -82-4·(-5)·1000
Δ = 20064
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:

$\sqrt{\Delta}=\sqrt{20064}=\sqrt{16*1254}=\sqrt{16}*\sqrt{1254}=4\sqrt{1254}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{1254}}{2*-5}=\frac{8-4\sqrt{1254}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{1254}}{2*-5}=\frac{8+4\sqrt{1254}}{-10}
$