50=((0.3+x)(0.4+x))/((0.1-x)(0.2-x))

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Solution for 50=((0.3+x)(0.4+x))/((0.1-x)(0.2-x)) equation: 


D( x )

(0.1-x)*(0.2-x) = 0

(0.1-x)*(0.2-x) = 0

(0.1-x)*(0.2-x) = 0

( 0.1-x )

0.1-x = 0 // - 0.1

-x = -0.1 // * -1

x = 0.1

( 0.2-x )

0.2-x = 0 // - 0.2

-x = -0.2 // * -1

x = 0.2

x in (-oo:0.1) U (0.1:0.2) U (0.2:+oo)

50 = ((x+0.3)*(x+0.4))/((0.1-x)*(0.2-x)) // - ((x+0.3)*(x+0.4))/((0.1-x)*(0.2-x))

50-(((x+0.3)*(x+0.4))/((0.1-x)*(0.2-x))) = 0

(-1*(x+0.3)*(x+0.4))/((0.1-x)*(0.2-x))+50 = 0

(-1*(x+0.3)*(x+0.4))/((0.1-x)*(0.2-x))+(50*(0.1-x)*(0.2-x))/((0.1-x)*(0.2-x)) = 0

50*(0.1-x)*(0.2-x)-1*(x+0.3)*(x+0.4) = 0

49*x^2-15.7*x+0.88 = 0

49*x^2-15.7*x+0.88 = 0

49*x^2-15.7*x+0.88 = 0

DELTA = (-15.7)^2-(0.88*4*49)

DELTA = 15.7^2-172.48

DELTA = 74.01

DELTA > 0

x = ((15.7^2-172.48)^(1/2)+15.7)/(2*49) or x = (15.7-(15.7^2-172.48)^(1/2))/(2*49)

x = ((15.7^2-172.48)^(1/2)+15.7)/98 or x = (15.7-(15.7^2-172.48)^(1/2))/98

(x-((15.7-(15.7^2-172.48)^(1/2))/98))*(x-(((15.7^2-172.48)^(1/2)+15.7)/98)) = 0

((x-((15.7-(15.7^2-172.48)^(1/2))/98))*(x-(((15.7^2-172.48)^(1/2)+15.7)/98)))/((0.1-x)*(0.2-x)) = 0

((x-((15.7-(15.7^2-172.48)^(1/2))/98))*(x-(((15.7^2-172.48)^(1/2)+15.7)/98)))/((0.1-x)*(0.2-x)) = 0 // * (0.1-x)*(0.2-x)

(x-((15.7-(15.7^2-172.48)^(1/2))/98))*(x-(((15.7^2-172.48)^(1/2)+15.7)/98)) = 0

( x-(((15.7^2-172.48)^(1/2)+15.7)/98) )

x-(((15.7^2-172.48)^(1/2)+15.7)/98) = 0 // + ((15.7^2-172.48)^(1/2)+15.7)/98

x = ((15.7^2-172.48)^(1/2)+15.7)/98

( x-((15.7-(15.7^2-172.48)^(1/2))/98) )

x-((15.7-(15.7^2-172.48)^(1/2))/98) = 0 // + (15.7-(15.7^2-172.48)^(1/2))/98

x = (15.7-(15.7^2-172.48)^(1/2))/98

x in { ((15.7^2-172.48)^(1/2)+15.7)/98, (15.7-(15.7^2-172.48)^(1/2))/98 }

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