(0.6x+19)/x=0.2x

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Solution for (0.6x+19)/x=0.2x equation: 


D( x )

x = 0

x = 0

x = 0

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

(0.6*x+19)/x = 0.2*x // - 0.2*x

(0.6*x+19)/x-(0.2*x) = 0

(0.6*x+19)/x-0.2*x = 0

(0.6*x+19)/x+(-0.2*x*x)/x = 0

0.6*x-0.2*x*x+19 = 0

0.6*x-0.2*x^2+19 = 0

0.6*x-0.2*x^2+19 = 0

0.6*x-0.2*x^2+19 = 0

DELTA = 0.6^2-(-0.2*4*19)

DELTA = 0.6^2+15.2

DELTA = 15.56

DELTA > 0

x = ((0.6^2+15.2)^(1/2)-0.6)/(-0.2*2) or x = (-(0.6^2+15.2)^(1/2)-0.6)/(-0.2*2)

x = -2.5*((0.6^2+15.2)^(1/2)-0.6) or x = 2.5*((0.6^2+15.2)^(1/2)+0.6)

(x+2.5*((0.6^2+15.2)^(1/2)-0.6))*(x-2.5*((0.6^2+15.2)^(1/2)+0.6)) = 0

((x+2.5*((0.6^2+15.2)^(1/2)-0.6))*(x-2.5*((0.6^2+15.2)^(1/2)+0.6)))/x = 0

((x+2.5*((0.6^2+15.2)^(1/2)-0.6))*(x-2.5*((0.6^2+15.2)^(1/2)+0.6)))/x = 0 // * x

(x+2.5*((0.6^2+15.2)^(1/2)-0.6))*(x-2.5*((0.6^2+15.2)^(1/2)+0.6)) = 0

( x+2.5*((0.6^2+15.2)^(1/2)-0.6) )

x+2.5*((0.6^2+15.2)^(1/2)-0.6) = 0 // - 2.5*((0.6^2+15.2)^(1/2)-0.6)

x = -(2.5*((0.6^2+15.2)^(1/2)-0.6))

x = -2.5*((0.6^2+15.2)^(1/2)-0.6)

( x-2.5*((0.6^2+15.2)^(1/2)+0.6) )

x-2.5*((0.6^2+15.2)^(1/2)+0.6) = 0 // + -2.5*((0.6^2+15.2)^(1/2)+0.6)

x = -(-2.5*((0.6^2+15.2)^(1/2)+0.6))

x = 2.5*((0.6^2+15.2)^(1/2)+0.6)

x in { -2.5*((0.6^2+15.2)^(1/2)-0.6), 2.5*((0.6^2+15.2)^(1/2)+0.6) }

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