F.4 maths Variation

a) Divide both sides by y^2, it becomes 3x^2/y^2 - 10x/y + 3 = 0
Solve the above quadratic equation, x/y = 3 or 1/3

b) (2x+3y)(2x-3y) = 6xy
4x^2 - 9y^2 = 6xy
Again, divide both sides by y^2, 4x^2/y^2 - 9 = 6x/y
4(x/y)^2 - 6(x/y) - 9 = 0
x/y = (3+3*5^(1/2))/4 or (3-3*5^(1/2))/4