6/(t^2)=2t^2+1

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Solution for 6/(t^2)=2t^2+1 equation: 


D( t )

t^2 = 0

t^2 = 0

t^2 = 0

1*t^2 = 0 // : 1

t^2 = 0

t = 0

t in (-oo:0) U (0:+oo)

6/(t^2) = 2*t^2+1 // - 2*t^2+1

6/(t^2)-(2*t^2)-1 = 0

6/(t^2)-2*t^2-1 = 0

6*t^-2-2*t^2-1 = 0

t_1 = t^2

6*t_1^-1-2*t_1^1-1 = 0

6*t_1^-1-2*t_1^1-1*t_1^0 = 0

(6*t_1^0-2*t_1^2-1*t_1^1)/(t_1^1) = 0 // * t_1^2

t_1^1*(6*t_1^0-2*t_1^2-1*t_1^1) = 0

t_1^1

6-2*t_1^2-t_1 = 0

6-2*t_1^2-t_1 = 0

DELTA = (-1)^2-(-2*4*6)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(-2*2) or t_1 = (1-49^(1/2))/(-2*2)

t_1 = -2 or t_1 = 3/2

t_1 in { -2, 3/2} 

t_1 = -2

t^2+2 = 0

1*t^2 = -2 // : 1

t^2 = -2

t_1 = 3/2

t^2-3/2 = 0

1*t^2 = 3/2 // : 1

t^2 = 3/2

t^2 = 3/2 // ^ 1/2

abs(t) = (3/2)^(1/2)

t = (3/2)^(1/2) or t = -(3/2)^(1/2)

t in { (3/2)^(1/2), -(3/2)^(1/2) }

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