10q=(200/q)+5q

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Solution for 10q=(200/q)+5q equation: 


D( q )

q = 0

q = 0

q = 0

q in (-oo:0) U (0:+oo)

10*q = 5*q+200/q // - 5*q+200/q

10*q-(5*q)-(200/q) = 0

10*q-5*q-200*q^-1 = 0

5*q^1-200*q^-1 = 0

(5*q^2-200*q^0)/(q^1) = 0 // * q^2

q^1*(5*q^2-200*q^0) = 0

q^1

5*q^2-200 = 0

5*q^2-200 = 0

DELTA = 0^2-(-200*4*5)

DELTA = 4000

DELTA > 0

q = (4000^(1/2)+0)/(2*5) or q = (0-4000^(1/2))/(2*5)

q = 2*10^(1/2) or q = -2*10^(1/2)

q in { -2*10^(1/2), 2*10^(1/2)} 

q in { -2*10^(1/2), 2*10^(1/2) }

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