1/4x^4-1/33x^2-27=0

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Solution for 1/4x^4-1/33x^2-27=0 equation: 


x in (-oo:+oo)

(1/4)*x^4-((1/33)*x^2)-27 = 0

(1/4)*x^4+(-1/33)*x^2-27 = 0

1/4*x^4-1/33*x^2-27 = 0

t_1 = x^2

1/4*t_1^2-1/33*t_1^1-27 = 0

1/4*t_1^2-1/33*t_1-27 = 0

DELTA = (-1/33)^2-(-27*1/4*4)

DELTA = 29404/1089

DELTA > 0

t_1 = ((29404/1089)^(1/2)+1/33)/(1/4*2) or t_1 = (1/33-(29404/1089)^(1/2))/(1/4*2)

t_1 = 2*((29404/1089)^(1/2)+1/33) or t_1 = 2*(1/33-(29404/1089)^(1/2))

t_1 = 2*(1/33-(29404/1089)^(1/2))

x^2-(2*(1/33-(29404/1089)^(1/2))) = 0

x^2-2*(1/33-(29404/1089)^(1/2)) = 0

1*x^2 = -(-2*(1/33-(29404/1089)^(1/2))) // : 1

x^2 = 2*(1/33-(29404/1089)^(1/2))

t_1 = 2*((29404/1089)^(1/2)+1/33)

x^2-(2*((29404/1089)^(1/2)+1/33)) = 0

x^2-2*((29404/1089)^(1/2)+1/33) = 0

1*x^2 = -(-2*((29404/1089)^(1/2)+1/33)) // : 1

x^2 = 2*((29404/1089)^(1/2)+1/33)

x^2 = 2*((29404/1089)^(1/2)+1/33) // ^ 1/2

abs(x) = 2^(1/2)*((29404/1089)^(1/2)+1/33)^(1/2)

x = 2^(1/2)*((29404/1089)^(1/2)+1/33)^(1/2) or x = -(2^(1/2)*((29404/1089)^(1/2)+1/33)^(1/2))

x in { 2^(1/2)*((29404/1089)^(1/2)+1/33)^(1/2), -(2^(1/2)*((29404/1089)^(1/2)+1/33)^(1/2)) }

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