Help for quickest and clearest route for differentiation question

[kauymatty]

Homework Statement

Find the coordinates of the points on these curves at which the gradient has the given values.

y=1/3x^(3/2)-x^(1/2), gradient=3/4

The Attempt at a Solution

Basically the problem I have isn't really finding the answer because...

x^(1/2)-x^-(1/2)=6/4[/b] and then from here I just used trial and error to find 4, but I want to know how I would follow it through with the algebra, i.e. only has x on one side as one term e.g. x= ans.


Thanks in advance,

kauymatty

 

[BAnders1]

Try substituting z = x^(1/2), then cast the result into the form az^2 + bz + c = 0.

 

[vela]

I'd square both sides of the equation. That'll eliminate the square roots completely.

 

[kauymatty]

I'd square both sides of the equation. That'll eliminate the square roots completely.

Thanks vela and banders, but after eliminating the roots I would still have the negative power, would I just get a common denominator by multiplying through with 16x as the denominator? (big of a noobish question XD)

 

[vela]

Multiplying through by 16x would be fine.