solve the equation 2x+3/x=-2 and express the roots in a+bi form?

2x + 3/x = -2
x(2x + 3/x) = x(-2)
2x^2 + 3 = -2x
2x^2 + 2x + 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 2
b = 2
c = 3

x = [-2 ±√(4 - 24)]/4
x = [-2 ±√(-20)]/4
x = [-2 ±√(2^2 * i^2 * 5)]/4
x = [-2 ±2i√5]/4
x = [-1 ±i√5]/2

∴ x = [-1 ±i√5]/2

The roots of 2x^2 + 2x + 3 = 0 are

-0.5 - 1.118i and

-0.5 + 1.118i

We meet again !
Reading this as :-
2x + (3/x) = - 2
2x² + 3 = - 2x
2x² + 2x + 3 = 0
x = [ - 2 ± √ (4 - 24 ) ] / 4
x = [ - 2 ± √ (- 20) ] / 4
x = [ - 2 ± i 2√5 ] / 4
x = [ -1 ± i √5 ] / 2

multiply all by x
2x^2+3+2x=0
2x^2+2x+3=0
D=4-4*2*3=-20=20*i^2
x=(-2+/-2i√5 )/4=(-1+/-i√5 )/2