Y=x^2-200x-480000

Solution for Y=x^2-200x-480000 equation:

=Y^2-200Y-480000

We move all terms to the left:

-(Y^2-200Y-480000)=0

We get rid of parentheses

-Y^2+200Y+480000=0

We add all the numbers together, and all the variables

-1Y^2+200Y+480000=0

a = -1; b = 200; c = +480000;
Δ = b2-4ac
Δ = 2002-4·(-1)·480000
Δ = 1960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1960000}=1400$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-1400}{2*-1}=\frac{-1600}{-2}
=+800
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+1400}{2*-1}=\frac{1200}{-2}
=-600
$