Make y the subject of the curve equation
y = -1/(2x)
Substitute for y in the line equation
2x +3(-1/2x) + 2 = 0
Multiply every term by 2x
4x^2 - 3 + 4x = 0
4x^2 + 4x - 3 = 0
(2x - 1)(2x + 3) = 0
If 2x - 1 = 0 then
2x = 1
x = 1/2
y = -1/(2 x 1/2) = -1
If 2x + 3 = 0 then
2x = -3
x = -1.5
y = -1/(2 x -1.5) = -1/3
The points of intersection are (1/2, -1) and (-1.5, -1/3)
Sorry about the mixture of fractions and decimals ;)
