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200x-2x=-x^2+5x+9000
We move all terms to the left:
200x-2x-(-x^2+5x+9000)=0
We add all the numbers together, and all the variables
-(-x^2+5x+9000)+198x=0
We get rid of parentheses
x^2-5x+198x-9000=0
We add all the numbers together, and all the variables
x^2+193x-9000=0
a = 1; b = 193; c = -9000;
Δ = b2-4ac
Δ = 1932-4·1·(-9000)
Δ = 73249
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(193)-\sqrt{73249}}{2*1}=\frac{-193-\sqrt{73249}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(193)+\sqrt{73249}}{2*1}=\frac{-193+\sqrt{73249}}{2} $
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