2x^2-288/x^2

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Solution for 2x^2-288/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

2*x^2-(288/(x^2)) = 0

2*x^2-288*x^-2 = 0

t_1 = x^2

2*t_1^1-288*t_1^-1 = 0

2*t_1^1-288*t_1^-1 = 0

(2*t_1^2-288*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^2-288*t_1^0) = 0

t_1^1

2*t_1^2-288 = 0

2*t_1^2-288 = 0

DELTA = 0^2-(-288*2*4)

DELTA = 2304

DELTA > 0

t_1 = (2304^(1/2)+0)/(2*2) or t_1 = (0-2304^(1/2))/(2*2)

t_1 = 12 or t_1 = -12

t_1 in { -12, 12} 

t_1 = -12

x^2+12 = 0

1*x^2 = -12 // : 1

x^2 = -12

t_1 = 12

x^2-12 = 0

1*x^2 = 12 // : 1

x^2 = 12

x^2 = 12 // ^ 1/2

abs(x) = 2*3^(1/2)

x = 2*3^(1/2) or x = -(2*3^(1/2))

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

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