100x-x^2-2400=0

Solution for 100x-x^2-2400=0 equation:

100x-x^2-2400=0

We add all the numbers together, and all the variables

-1x^2+100x-2400=0

a = -1; b = 100; c = -2400;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2400)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20}{2*-1}=\frac{-120}{-2}
=+60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20}{2*-1}=\frac{-80}{-2}
=+40
$