3.92=(4x^2)/(0.5-x)

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Solution for 3.92=(4x^2)/(0.5-x) equation: 


D( x )

0.5-x = 0

0.5-x = 0

0.5-x = 0

0.5-x = 0 // - 0.5

-x = -0.5 // * -1

x = 0.5

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

3.92 = (4*x^2)/(0.5-x) // - (4*x^2)/(0.5-x)

3.92-((4*x^2)/(0.5-x)) = 0

3.92-4*x^2*(0.5-x)^-1 = 0

(-4*x^2)/(0.5-x)+3.92 = 0

(-4*x^2)/(0.5-x)+(3.92*(0.5-x))/(0.5-x) = 0

3.92*(0.5-x)-4*x^2 = 0

1.96-4*x^2-3.92*x = 0

1.96-4*x^2-3.92*x = 0

1.96-4*x^2-3.92*x = 0

DELTA = (-3.92)^2-(-4*1.96*4)

DELTA = 3.92^2+31.36

DELTA = 46.7264

DELTA > 0

x = ((3.92^2+31.36)^(1/2)+3.92)/(-4*2) or x = (3.92-(3.92^2+31.36)^(1/2))/(-4*2)

x = ((3.92^2+31.36)^(1/2)+3.92)/(-8) or x = (3.92-(3.92^2+31.36)^(1/2))/(-8)

(x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)))*(x-((3.92-(3.92^2+31.36)^(1/2))/(-8))) = 0

((x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)))*(x-((3.92-(3.92^2+31.36)^(1/2))/(-8))))/(0.5-x) = 0

((x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)))*(x-((3.92-(3.92^2+31.36)^(1/2))/(-8))))/(0.5-x) = 0 // * 0.5-x

(x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)))*(x-((3.92-(3.92^2+31.36)^(1/2))/(-8))) = 0

( x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)) )

x-(((3.92^2+31.36)^(1/2)+3.92)/(-8)) = 0 // + ((3.92^2+31.36)^(1/2)+3.92)/(-8)

x = ((3.92^2+31.36)^(1/2)+3.92)/(-8)

( x-((3.92-(3.92^2+31.36)^(1/2))/(-8)) )

x-((3.92-(3.92^2+31.36)^(1/2))/(-8)) = 0 // + (3.92-(3.92^2+31.36)^(1/2))/(-8)

x = (3.92-(3.92^2+31.36)^(1/2))/(-8)

x in { ((3.92^2+31.36)^(1/2)+3.92)/(-8), (3.92-(3.92^2+31.36)^(1/2))/(-8) }

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