n^2+45n=1000

Solution for n^2+45n=1000 equation:

n^2+45n=1000

We move all terms to the left:

n^2+45n-(1000)=0

a = 1; b = 45; c = -1000;
Δ = b2-4ac
Δ = 452-4·1·(-1000)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{241}}{2*1}=\frac{-45-5\sqrt{241}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{241}}{2*1}=\frac{-45+5\sqrt{241}}{2}
$