3x-2=5(1-9x^2)^1/2

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Solution for 3x-2=5(1-9x^2)^1/2 equation: 


x in (-oo:+oo)

3*x-2 = (5*(1-(9*x^2))^1)/2 // - (5*(1-(9*x^2))^1)/2

3*x-((5*(1-(9*x^2))^1)/2)-2 = 0

(-5/2)*(1-9*x^2)+3*x-2 = 0

3*x-5/2*(1-9*x^2)-2 = 0

3*x-5/2*(1-9*x^2)-2 = 0

45/2*x^2+3*x-5/2-2 = 0

45/2*x^2+3*x-9/2 = 0

45/2*x^2+3*x-9/2 = 0

3*(15/2*x^2+x-3/2) = 0

15/2*x^2+x-3/2 = 0

DELTA = 1^2-(-3/2*4*15/2)

DELTA = 46

DELTA > 0

x = (46^(1/2)-1)/(2*15/2) or x = (-46^(1/2)-1)/(2*15/2)

x = (46^(1/2)-1)/15 or x = (-(46^(1/2)+1))/15

3*(x+(46^(1/2)+1)/15)*(x-((46^(1/2)-1)/15)) = 0

3*(x+(46^(1/2)+1)/15)*(x-((46^(1/2)-1)/15)) = 0

( x+(46^(1/2)+1)/15 )

x+(46^(1/2)+1)/15 = 0 // - (46^(1/2)+1)/15

x = -((46^(1/2)+1)/15)

( x-((46^(1/2)-1)/15) )

x-((46^(1/2)-1)/15) = 0 // + (46^(1/2)-1)/15

x = (46^(1/2)-1)/15

x in { -((46^(1/2)+1)/15), (46^(1/2)-1)/15 }

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