We have, x2−2x+

3

2

= 0
Comparing the given equation with the general form ax2 + bx + c = 0,
we get a = 1 b = − 2 , c =

3

2

∴ x =

−b±√b2−4ac

2a

=

2±√(−2)2−4×1× 3 2

2×1

=

2±√4−6

2

=

2±√−2

2

=

2±√2

2

= 1 ±

√2

2

i