solve 3x^2+xy+4y^2-9=0 for x in terms of y

Answer 1

compare
3x^2+xy+4y^2-9=0 with
ax^2 + bx + c = 0

you have
a = 3
b = y
c = 4y^2-9

x = (-y ± √(y^2 - 4(3)(4y^2-9))/6
= (-y ± √(108 - 11y^2)/6