We have , x2+x+

1

√2

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

1

√2

∴ x =

−b±√b2−4ac

2a

=

−1±√(1)2−4×1× 1 √2

2.1

=

−1±√1−2√2

2

=

−1±√−(2√2)−1)

2

=

−1±i√(2√2−1)

2

∴ The roots of the given equation are

−1+i√(2√2−1)

2

and

−1−i√(2√2−1)

2