1/x^2=0.75/(0.5-x)^2

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Solution for 1/x^2=0.75/(0.5-x)^2 equation: 


D( x )

(0.5-x)^2 = 0

x^2 = 0

(0.5-x)^2 = 0

(0.5-x)^2 = 0

0.5-x = 0 // - 0.5

-x = -0.5 // * -1

x = 0.5

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:0.5) U (0.5:+oo)

1/(x^2) = 0.75/((0.5-x)^2) // - 0.75/((0.5-x)^2)

1/(x^2)-(0.75/((0.5-x)^2)) = 0

1/(x^2)-0.75*(0.5-x)^-2 = 0

1/(x^2)-0.75/((0.5-x)^2) = 0

(-0.75*x^2)/(x^2*(0.5-x)^2)+(1*(0.5-x)^2)/(x^2*(0.5-x)^2) = 0

1*(0.5-x)^2-0.75*x^2 = 0

0.25*x^2-x+0.25 = 0

0.25*x^2-x+0.25 = 0

0.25*x^2-x+0.25 = 0

DELTA = (-1)^2-(0.25*0.25*4)

DELTA = 0.75

DELTA > 0

x = (0.75^(1/2)+1)/(0.25*2) or x = (1-0.75^(1/2))/(0.25*2)

x = 2*(0.75^(1/2)+1) or x = 2*(1-0.75^(1/2))

(x-2*(1-0.75^(1/2)))*(x-2*(0.75^(1/2)+1)) = 0

((x-2*(1-0.75^(1/2)))*(x-2*(0.75^(1/2)+1)))/(x^2*(0.5-x)^2) = 0

((x-2*(1-0.75^(1/2)))*(x-2*(0.75^(1/2)+1)))/(x^2*(0.5-x)^2) = 0 // * x^2*(0.5-x)^2

(x-2*(1-0.75^(1/2)))*(x-2*(0.75^(1/2)+1)) = 0

( x-2*(0.75^(1/2)+1) )

x-2*(0.75^(1/2)+1) = 0 // + -2*(0.75^(1/2)+1)

x = -(-2*(0.75^(1/2)+1))

x = 2*(0.75^(1/2)+1)

( x-2*(1-0.75^(1/2)) )

x-2*(1-0.75^(1/2)) = 0 // + -2*(1-0.75^(1/2))

x = -(-2*(1-0.75^(1/2)))

x = 2*(1-0.75^(1/2))

x in { 2*(0.75^(1/2)+1), 2*(1-0.75^(1/2)) }

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