((2)(19)/x^2)=((3)(19)/(0.40-x)^2)

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Solution for ((2)(19)/x^2)=((3)(19)/(0.40-x)^2) equation: 


D( x )

(0.4-x)^2 = 0

x^2 = 0

(0.4-x)^2 = 0

(0.4-x)^2 = 0

0.4-x = 0 // - 0.4

-x = -0.4 // * -1

x = 0.4

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:0.4) U (0.4:+oo)

(2*19)/(x^2) = (3*19)/((0.4-x)^2) // - (3*19)/((0.4-x)^2)

(2*19)/(x^2)-((3*19)/((0.4-x)^2)) = 0

(2*19)/(x^2)-57*(0.4-x)^-2 = 0

38/(x^2)-57/((0.4-x)^2) = 0

(-57*x^2)/(x^2*(0.4-x)^2)+(38*(0.4-x)^2)/(x^2*(0.4-x)^2) = 0

38*(0.4-x)^2-57*x^2 = 0

6.08-19*x^2-30.4*x = 0

6.08-19*x^2-30.4*x = 0

6.08-19*x^2-30.4*x = 0

DELTA = (-30.4)^2-(-19*4*6.08)

DELTA = 30.4^2+462.08

DELTA = 1386.24

DELTA > 0

x = ((30.4^2+462.08)^(1/2)+30.4)/(-19*2) or x = (30.4-(30.4^2+462.08)^(1/2))/(-19*2)

x = ((30.4^2+462.08)^(1/2)+30.4)/(-38) or x = (30.4-(30.4^2+462.08)^(1/2))/(-38)

(x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)))*(x-((30.4-(30.4^2+462.08)^(1/2))/(-38))) = 0

((x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)))*(x-((30.4-(30.4^2+462.08)^(1/2))/(-38))))/(x^2*(0.4-x)^2) = 0

((x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)))*(x-((30.4-(30.4^2+462.08)^(1/2))/(-38))))/(x^2*(0.4-x)^2) = 0 // * x^2*(0.4-x)^2

(x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)))*(x-((30.4-(30.4^2+462.08)^(1/2))/(-38))) = 0

( x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)) )

x-(((30.4^2+462.08)^(1/2)+30.4)/(-38)) = 0 // + ((30.4^2+462.08)^(1/2)+30.4)/(-38)

x = ((30.4^2+462.08)^(1/2)+30.4)/(-38)

( x-((30.4-(30.4^2+462.08)^(1/2))/(-38)) )

x-((30.4-(30.4^2+462.08)^(1/2))/(-38)) = 0 // + (30.4-(30.4^2+462.08)^(1/2))/(-38)

x = (30.4-(30.4^2+462.08)^(1/2))/(-38)

x in { ((30.4^2+462.08)^(1/2)+30.4)/(-38), (30.4-(30.4^2+462.08)^(1/2))/(-38) }

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