6x^(1/2)=14x^(1/4)-8

Solution for 6x^(1/2)=14x^(1/4)-8 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

6*x^(1/2) = 14*x^(1/4)-8 // - 14*x^(1/4)-8

6*x^(1/2)-(14*x^(1/4))+8 = 0

6*x^(1/2)-14*x^(1/4)+8 = 0

t_1 = x^(1/4)

6*t_1^2-14*t_1^1+8 = 0

6*t_1^2-14*t_1+8 = 0

DELTA = (-14)^2-(4*6*8)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)+14)/(2*6) or t_1 = (14-4^(1/2))/(2*6)

t_1 = 4/3 or t_1 = 1

t_1 = 1

x^(1/4)-1 = 0

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

x^(1/4) = 1

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

x = 1

t_1 = 4/3

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

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

x^(1/4) = 4/3

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

x = 256/81

x in { 1, 256/81 }