200x-x^2=5x+9000

Solution for 200x-x^2=5x+9000 equation:

200x-x^2=5x+9000

We move all terms to the left:

200x-x^2-(5x+9000)=0

We add all the numbers together, and all the variables

-1x^2+200x-(5x+9000)=0

We get rid of parentheses

-1x^2+200x-5x-9000=0

We add all the numbers together, and all the variables

-1x^2+195x-9000=0

a = -1; b = 195; c = -9000;
Δ = b2-4ac
Δ = 1952-4·(-1)·(-9000)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-45}{2*-1}=\frac{-240}{-2}
=+120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+45}{2*-1}=\frac{-150}{-2}
=+75
$