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4*3y + 5*sqrt(3y) - 21 = 0.
Introduce new variable x = sqrt(3y). Then your equations takes the form
= 0.
Apply the quadratic formula
= = = .
1. = = ---> = ---> 3y = = ---> y = = .
2. = = -3 ---> = -3 ---> 3y = = 9 ---> y = = 3.
The root y = satisfies the original equation.
The root y = 3 does not satisfy. It is EXTRANEOUS root (it is not the solution).
Answer. y = .
There is another way to solve the original equation by isolating the term and then squaring both sides.
It should lead to the same result.
Plot y =