(0.65-x)^2/x=68

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Solution for (0.65-x)^2/x=68 equation:


D( x )

x = 0

x = 0

x = 0

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

((0.65-x)^2)/x = 68 // - 68

((0.65-x)^2)/x-68 = 0

((0.65-x)^2)/x+(-68*x)/x = 0

(0.65-x)^2-68*x = 0

x^2-69.3*x+0.4225 = 0

x^2-69.3*x+0.4225 = 0

x^2-69.3*x+0.4225 = 0

DELTA = (-69.3)^2-(0.4225*1*4)

DELTA = 69.3^2-1.69

DELTA = 4800.8

DELTA > 0

x = ((69.3^2-1.69)^(1/2)+69.3)/(1*2) or x = (69.3-(69.3^2-1.69)^(1/2))/(1*2)

x = ((69.3^2-1.69)^(1/2)+69.3)/2 or x = (69.3-(69.3^2-1.69)^(1/2))/2

(x-((69.3-(69.3^2-1.69)^(1/2))/2))*(x-(((69.3^2-1.69)^(1/2)+69.3)/2)) = 0

((x-((69.3-(69.3^2-1.69)^(1/2))/2))*(x-(((69.3^2-1.69)^(1/2)+69.3)/2)))/x = 0

((x-((69.3-(69.3^2-1.69)^(1/2))/2))*(x-(((69.3^2-1.69)^(1/2)+69.3)/2)))/x = 0 // * x

(x-((69.3-(69.3^2-1.69)^(1/2))/2))*(x-(((69.3^2-1.69)^(1/2)+69.3)/2)) = 0

( x-(((69.3^2-1.69)^(1/2)+69.3)/2) )

x-(((69.3^2-1.69)^(1/2)+69.3)/2) = 0 // + ((69.3^2-1.69)^(1/2)+69.3)/2

x = ((69.3^2-1.69)^(1/2)+69.3)/2

( x-((69.3-(69.3^2-1.69)^(1/2))/2) )

x-((69.3-(69.3^2-1.69)^(1/2))/2) = 0 // + (69.3-(69.3^2-1.69)^(1/2))/2

x = (69.3-(69.3^2-1.69)^(1/2))/2

x in { ((69.3^2-1.69)^(1/2)+69.3)/2, (69.3-(69.3^2-1.69)^(1/2))/2 }

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