I hate fractions, so multiply through by 6. Factor out x^{1/2} on the right. Square each side. Expand the squared terms, distribute the x, subtract 36y^{2} from each side and apply the cubic formula (I don't know what it is but I know it exists).
Please use parentheses to make your meaning clear.
In a bit more detail, what he said was: multiply the equation by 6 to get
6y= 4x^(3/2)- 3x^(1/2)= (4x- 3)x^(1/2)
so
36y^2= (4x-3)^2(x)= (16x^2- 24x+ 9)x
= 16x^3- 24x^2+ 9x
Which you can write as 16x^3- 24x^2+ 9x- 36y^2= 0 and solve as a cubic equation.
(You can see I have absolutely nothing to do this morning. Well, nothing I want to do!)
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