-18/x^2-11=x^2

Solution for -18/x^2-11=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)

-18/(x^2)-11 = x^2 // - x^2

-x^2-18/(x^2)-11 = 0

-x^2-18*x^-2-11 = 0

t_1 = x^2

-1*t_1^1-18*t_1^-1-11 = 0

-1*t_1^1-18*t_1^-1-11*t_1^0 = 0

(-1*t_1^2-11*t_1^1-18*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(-1*t_1^2-11*t_1^1-18*t_1^0) = 0

t_1^1

-t_1^2-11*t_1-18 = 0

-t_1^2-11*t_1-18 = 0

DELTA = (-11)^2-(-18*(-1)*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+11)/(-1*2) or t_1 = (11-49^(1/2))/(-1*2)

t_1 = -9 or t_1 = -2

t_1 in { -9, -2} 

t_1 = -9

x^2+9 = 0

1*x^2 = -9 // : 1

x^2 = -9

t_1 = -2

x^2+2 = 0

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

x^2 = -2

x belongs to the empty set