Question 290479
Given

9x^2-4y^2=36
it can be written as

(3x)^2-(2y)^2=36
or
(3x-2y)(3x+2y)=36       because a^2-b^2=(a-b)(a+b)

now also it is given that 5x + 2y = 0 or 2y = -5x

replace this vlaue in the above equation we get

(3x + 5x)(3x - 5x)=36
-16x^2 =36
x = (3/2)i, -(3/2)i

putting values of x in 2y = -5x we get

(-3/2i , 15/4i), (3/2i, -15/4i)