-n^2+580n-48000=0

Solution for -n^2+580n-48000=0 equation:

-n^2+580n-48000=0

We add all the numbers together, and all the variables

-1n^2+580n-48000=0

a = -1; b = 580; c = -48000;
Δ = b2-4ac
Δ = 5802-4·(-1)·(-48000)
Δ = 144400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144400}=380$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(580)-380}{2*-1}=\frac{-960}{-2}
=+480
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(580)+380}{2*-1}=\frac{-200}{-2}
=+100
$