49.5=(2*x)/(0.2-x)^2

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Solution for 49.5=(2*x)/(0.2-x)^2 equation: 


D( x )

(0.2-x)^2 = 0

(0.2-x)^2 = 0

(0.2-x)^2 = 0

0.2-x = 0 // - 0.2

-x = -0.2 // * -1

x = 0.2

x in (-oo:0.2) U (0.2:+oo)

49.5 = (2*x)/((0.2-x)^2) // - (2*x)/((0.2-x)^2)

49.5-((2*x)/((0.2-x)^2)) = 0

49.5-2*x*(0.2-x)^-2 = 0

(-2*x)/((0.2-x)^2)+49.5 = 0

(-2*x)/((0.2-x)^2)+(49.5*(0.2-x)^2)/((0.2-x)^2) = 0

49.5*(0.2-x)^2-2*x = 0

49.5*x^2-21.8*x+1.98 = 0

49.5*x^2-21.8*x+1.98 = 0

49.5*x^2-21.8*x+1.98 = 0

DELTA = (-21.8)^2-(1.98*4*49.5)

DELTA = 21.8^2-392.04

DELTA = 83.2

DELTA > 0

x = ((21.8^2-392.04)^(1/2)+21.8)/(2*49.5) or x = (21.8-(21.8^2-392.04)^(1/2))/(2*49.5)

x = ((21.8^2-392.04)^(1/2)+21.8)/99 or x = (21.8-(21.8^2-392.04)^(1/2))/99

(x-((21.8-(21.8^2-392.04)^(1/2))/99))*(x-(((21.8^2-392.04)^(1/2)+21.8)/99)) = 0

((x-((21.8-(21.8^2-392.04)^(1/2))/99))*(x-(((21.8^2-392.04)^(1/2)+21.8)/99)))/((0.2-x)^2) = 0

((x-((21.8-(21.8^2-392.04)^(1/2))/99))*(x-(((21.8^2-392.04)^(1/2)+21.8)/99)))/((0.2-x)^2) = 0 // * (0.2-x)^2

(x-((21.8-(21.8^2-392.04)^(1/2))/99))*(x-(((21.8^2-392.04)^(1/2)+21.8)/99)) = 0

( x-(((21.8^2-392.04)^(1/2)+21.8)/99) )

x-(((21.8^2-392.04)^(1/2)+21.8)/99) = 0 // + ((21.8^2-392.04)^(1/2)+21.8)/99

x = ((21.8^2-392.04)^(1/2)+21.8)/99

( x-((21.8-(21.8^2-392.04)^(1/2))/99) )

x-((21.8-(21.8^2-392.04)^(1/2))/99) = 0 // + (21.8-(21.8^2-392.04)^(1/2))/99

x = (21.8-(21.8^2-392.04)^(1/2))/99

x in { ((21.8^2-392.04)^(1/2)+21.8)/99, (21.8-(21.8^2-392.04)^(1/2))/99 }

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