100x^(1/2)-75x^2=0

Solution for 100x^(1/2)-75x^2=0 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

100*x^(1/2)-(75*x^2) = 0

100*x^(1/2)-75*x^2 = 0

t_1 = x^(1/2)

100*t_1^1-75*t_1^4 = 0

100*t_1-75*t_1^4 = 0

25*t_1*(4-3*t_1^3) = 0

-3*t_1^3 = -4 // : -3

t_1^3 = 4/3

t_1^3 = 4/3 // ^ 1/3

t_1 = (4/3)^(1/3)

25*t_1 = 0

25*t_1 = 0 // : 25

t_1 = 0

t_1 = (4/3)^(1/3)

x^(1/2)-(4/3)^(1/3) = 0

1*x^(1/2) = (4/3)^(1/3) // : 1

x^(1/2) = (4/3)^(1/3)

x^(1/2) = (4/3)^(1/3) // ^ 2

x = (4/3)^(2/3)

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in { (4/3)^(2/3), 0 }