x/(5-2x)^2=20.5

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Solution for x/(5-2x)^2=20.5 equation:


D( x )

(5-(2*x))^2 = 0

(5-(2*x))^2 = 0

(5-(2*x))^2 = 0

(5-2*x)^2 = 0

5-2*x = 0 // - 5

-2*x = -5 // : -2

x = -5/(-2)

x = 5/2

x in (-oo:5/2) U (5/2:+oo)

x/((5-(2*x))^2) = 20.5 // - 20.5

x/((5-(2*x))^2)-20.5 = 0

x/((5-2*x)^2)-20.5 = 0

x/((5-2*x)^2)+(-20.5*(5-2*x)^2)/((5-2*x)^2) = 0

x-20.5*(5-2*x)^2 = 0

411*x-82*x^2-512.5 = 0

411*x-82*x^2-512.5 = 0

411*x-82*x^2-512.5 = 0

DELTA = 411^2-(-512.5*(-82)*4)

DELTA = 821

DELTA > 0

x = (821^(1/2)-411)/(-82*2) or x = (-821^(1/2)-411)/(-82*2)

x = (821^(1/2)-411)/(-164) or x = (821^(1/2)+411)/164

(x-((821^(1/2)-411)/(-164)))*(x-((821^(1/2)+411)/164)) = 0

((x-((821^(1/2)-411)/(-164)))*(x-((821^(1/2)+411)/164)))/((5-2*x)^2) = 0

((x-((821^(1/2)-411)/(-164)))*(x-((821^(1/2)+411)/164)))/((5-2*x)^2) = 0 // * (5-2*x)^2

(x-((821^(1/2)-411)/(-164)))*(x-((821^(1/2)+411)/164)) = 0

( x-((821^(1/2)+411)/164) )

x-((821^(1/2)+411)/164) = 0 // + (821^(1/2)+411)/164

x = (821^(1/2)+411)/164

( x-((821^(1/2)-411)/(-164)) )

x-((821^(1/2)-411)/(-164)) = 0 // + (821^(1/2)-411)/(-164)

x = (821^(1/2)-411)/(-164)

x in { (821^(1/2)+411)/164, (821^(1/2)-411)/(-164) }

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