Given equation is
x 2 −x+2=0 .
Any equation of the form a x 2 +bx+c=0 has the solution
x= −b± D 2a
Here, D= b 2 −4ac is called the discriminant of the quadratic equation.
Therefore,
x= −( −1 )± 1−8 2 = 1± 7 i 2
Thus, x= 1± 7 i 2 .