5x^2-45/x^2-16

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Solution for 5x^2-45/x^2-16 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)

5*x^2-(45/(x^2))-16 = 0

5*x^2-45*x^-2-16 = 0

t_1 = x^2

5*t_1^1-45*t_1^-1-16 = 0

5*t_1^1-45*t_1^-1-16*t_1^0 = 0

(5*t_1^2-16*t_1^1-45*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(5*t_1^2-16*t_1^1-45*t_1^0) = 0

t_1^1

5*t_1^2-16*t_1-45 = 0

5*t_1^2-16*t_1-45 = 0

DELTA = (-16)^2-(-45*4*5)

DELTA = 256+900

DELTA = 1156

DELTA > 0

t_1 = ((256+900)^(1/2)+16)/(2*5) or t_1 = (16-(256+900)^(1/2))/(2*5)

t_1 = (16+34)/10 or t_1 = (16-34)/10

t_1 in { (16-34)/10, (16+34)/10} 

t_1 = (16-34)/10

x^2-((16-34)/10) = 0

1*x^2 = (16-34)/10 // : 1

x^2 = (16-34)/10

t_1 = (16+34)/10

x^2-((16+34)/10) = 0

1*x^2 = (16+34)/10 // : 1

x^2 = (16+34)/10

x^2 = (16+34)/10 // ^ 1/2

abs(x) = ((16+34)^(1/2))/(10^(1/2))

x = ((16+34)^(1/2))/(10^(1/2)) or x = -(((16+34)^(1/2))/(10^(1/2)))

x in { ((16+34)^(1/2))/(10^(1/2)), -(((16+34)^(1/2))/(10^(1/2))) }

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