X=500x+-2x2

Solution for X=500x+-2x2 equation:

X=500X+-2X^2

We move all terms to the left:

X-(500X+-2X^2)=0

We use the square of the difference formula

-(500X-2X^2)+X=0

We get rid of parentheses

2X^2-500X+X=0

We add all the numbers together, and all the variables

2X^2-499X=0

a = 2; b = -499; c = 0;
Δ = b2-4ac
Δ = -4992-4·2·0
Δ = 249001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{249001}=499$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-499)-499}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+499}{2*2}=\frac{998}{4}
=249+1/2
$