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Given utility function U = x*y^(1/2), solve for x and y that provide max utility (optimal x and y) and find the value of lambda.

Given utility function U = x*y^(1/2), solve for x and y that provide max utility (optimal x and y) and find the value of lambda. For FOCs I have y=4x^2 , x = (1/2)y^(1/2) , and 300-10x-5y=0 To solve for x and y, assuming these are quadratics? Not sure how to proceed to get x* and y*

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