45-9x^(1/2)=x-5

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Solution for 45-9x^(1/2)=x-5 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

45-(9*x^(1/2)) = x-5 // - x-5

5-x-(9*x^(1/2))+45 = 0

5-x-9*x^(1/2)+45 = 0

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

t_1 = x^(1/2)

50-1*t_1^2-9*t_1^1 = 0

50-t_1^2-9*t_1 = 0

DELTA = (-9)^2-(-1*4*50)

DELTA = 281

DELTA > 0

t_1 = (281^(1/2)+9)/(-1*2) or t_1 = (9-281^(1/2))/(-1*2)

t_1 = (281^(1/2)+9)/(-2) or t_1 = (9-281^(1/2))/(-2)

t_1 = (281^(1/2)+9)/(-2)

x^(1/2)-((281^(1/2)+9)/(-2)) = 0

1*x^(1/2) = (281^(1/2)+9)/(-2) // : 1

x^(1/2) = (281^(1/2)+9)/(-2)

( (281^(1/2)+9)/(-2) < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (9-281^(1/2))/(-2)

x^(1/2)-((9-281^(1/2))/(-2)) = 0

1*x^(1/2) = (9-281^(1/2))/(-2) // : 1

x^(1/2) = (9-281^(1/2))/(-2)

x^(1/2) = (9-281^(1/2))/(-2) // ^ 2

x = ((9-281^(1/2))^2)/4

x = ((9-281^(1/2))^2)/4

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