-20000+540x-x^2=0

Solution for -20000+540x-x^2=0 equation:

-20000+540x-x^2=0

We add all the numbers together, and all the variables

-1x^2+540x-20000=0

a = -1; b = 540; c = -20000;
Δ = b2-4ac
Δ = 5402-4·(-1)·(-20000)
Δ = 211600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{211600}=460$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-460}{2*-1}=\frac{-1000}{-2}
=+500
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+460}{2*-1}=\frac{-80}{-2}
=+40
$