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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 $
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