-5/x=3x+2;

Solve for x (note x ≠ 0 since x is in the denominator).

-5/x = 3x + 2 Multiply both sides by x: -5 = 3x^2 + 2x Rearrange: 3x^2 + 2x + 5 = 0

Discriminant: Δ = 2^2 - 4·3·5 = 4 - 60 = -56 < 0

• No real solutions.
• Complex solutions: x = (-2 ± i√56) / 6 = (-1 ± i√14) / 3

So, no real solutions; complex solutions are (-1 ± i√14)/3.