3x-((5x)^(1/2))-28=0

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Solution for 3x-((5x)^(1/2))-28=0 equation: 


D( x )

5*x < 0

5*x < 0

5*x < 0

5*x+0 < 0 // - 0

5*x < 0 // : 5

x < 0/5

x < 0

x in <0:+oo)

3*x-(5*x)^(1/2)-28 = 0

3*x-5^(1/2)*x^(1/2)-28 = 0

t_1 = x^(1/2)

3*t_1^2-5^(1/2)*t_1^1-28 = 0

3*t_1^2-5^(1/2)*t_1-28 = 0

DELTA = (-5^(1/2))^2-(-28*3*4)

DELTA = 341

DELTA > 0

t_1 = (5^(1/2)+341^(1/2))/(2*3) or t_1 = (5^(1/2)-341^(1/2))/(2*3)

t_1 = (5^(1/2)+341^(1/2))/6 or t_1 = (5^(1/2)-341^(1/2))/6

t_1 = (5^(1/2)-341^(1/2))/6

x^(1/2)-((5^(1/2)-341^(1/2))/6) = 0

1*x^(1/2) = (5^(1/2)-341^(1/2))/6 // : 1

x^(1/2) = (5^(1/2)-341^(1/2))/6

( (5^(1/2)-341^(1/2))/6 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (5^(1/2)+341^(1/2))/6

x^(1/2)-((5^(1/2)+341^(1/2))/6) = 0

1*x^(1/2) = (5^(1/2)+341^(1/2))/6 // : 1

x^(1/2) = (5^(1/2)+341^(1/2))/6

x^(1/2) = (5^(1/2)+341^(1/2))/6 // ^ 2

x = ((5^(1/2)+341^(1/2))^2)/36

x = ((5^(1/2)+341^(1/2))^2)/36

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