(2x)^2/(0.25-x)=0.05

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Solution for (2x)^2/(0.25-x)=0.05 equation: 


D( x )

0.25-x = 0

0.25-x = 0

0.25-x = 0

0.25-x = 0 // - 0.25

-x = -0.25 // * -1

x = 0.25

x in (-oo:0.25) U (0.25:+oo)

((2*x)^2)/(0.25-x) = 0.05 // - 0.05

((2*x)^2)/(0.25-x)-0.05 = 0

(4*x^2)/(0.25-x)-0.05 = 0

(4*x^2)/(0.25-x)+(-0.05*(0.25-x))/(0.25-x) = 0

4*x^2-0.05*(0.25-x) = 0

4*x^2+0.05*x-0.0125 = 0

4*x^2+0.05*x-0.0125 = 0

4*x^2+0.05*x-0.0125 = 0

DELTA = 0.05^2-(-0.0125*4*4)

DELTA = 0.05^2+0.2

DELTA = 0.2025

DELTA > 0

x = ((0.05^2+0.2)^(1/2)-0.05)/(2*4) or x = (-(0.05^2+0.2)^(1/2)-0.05)/(2*4)

x = ((0.05^2+0.2)^(1/2)-0.05)/8 or x = (-((0.05^2+0.2)^(1/2)+0.05))/8

(x+((0.05^2+0.2)^(1/2)+0.05)/8)*(x-(((0.05^2+0.2)^(1/2)-0.05)/8)) = 0

((x+((0.05^2+0.2)^(1/2)+0.05)/8)*(x-(((0.05^2+0.2)^(1/2)-0.05)/8)))/(0.25-x) = 0

((x+((0.05^2+0.2)^(1/2)+0.05)/8)*(x-(((0.05^2+0.2)^(1/2)-0.05)/8)))/(0.25-x) = 0 // * 0.25-x

(x+((0.05^2+0.2)^(1/2)+0.05)/8)*(x-(((0.05^2+0.2)^(1/2)-0.05)/8)) = 0

( x+((0.05^2+0.2)^(1/2)+0.05)/8 )

x+((0.05^2+0.2)^(1/2)+0.05)/8 = 0 // - ((0.05^2+0.2)^(1/2)+0.05)/8

x = -(((0.05^2+0.2)^(1/2)+0.05)/8)

( x-(((0.05^2+0.2)^(1/2)-0.05)/8) )

x-(((0.05^2+0.2)^(1/2)-0.05)/8) = 0 // + ((0.05^2+0.2)^(1/2)-0.05)/8

x = ((0.05^2+0.2)^(1/2)-0.05)/8

x in { -(((0.05^2+0.2)^(1/2)+0.05)/8), ((0.05^2+0.2)^(1/2)-0.05)/8 }

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