(12-4x)^(1/2)=x

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Solution for (12-4x)^(1/2)=x equation:


D( x )

12-(4*x) < 0

12-(4*x) < 0

12-(4*x) < 0

12-4*x < 0

12-4*x < 0 // - 12

-4*x < -12 // : -4

x > -12/(-4)

x > 3

x in (-oo:3>

(12-(4*x))^(1/2) = x // - x

(12-(4*x))^(1/2)-x = 0

(12-4*x)^(1/2)-x = 0

(12-4*x)^(1/2) = -x // + x

(12-4*x)^(1/2) = x // ^ 2

abs(12-4*x) = x^2 // - x^2

abs(12-4*x)-x^2 = 0

x in (-oo:+oo)

abs(12-4*x)

12-4*x >= 0

12-4*x >= 0 // - 12

-4*x >= -12 // : -4

x <= -12/(-4)

x <= 3

x in (-oo:3>

12-x^2-4*x = 0

x in (3:+oo)

-x^2-(-4*x)-12 = 0

abs(12-4*x)-x^2 = 0

/ | 12-x^2-4*x = 0 i x in (-oo:3> | -x^2-(-4*x)-12 = 0 i x in (3:+oo)

x in (-oo:3>

12-x^2-4*x = 0

DELTA = (-4)^2-(-1*4*12)

DELTA = 64

DELTA > 0

x = (64^(1/2)+4)/(-1*2) or x = (4-64^(1/2))/(-1*2)

x = -6 or x = 2

x in (3:+oo)

-x^2-(-4*x)-12 = 0

4*x-x^2-12 = 0

DELTA = 4^2-(-12*(-1)*4)

DELTA = -32

DELTA < 0

x in { -6, 2 }

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