Find Solutions of the equation x23x80 expressed in abi form

Find Solutions of the equation x^2+3x+8=0 expressed in a+bi form

x^2 + 3x +8 = 0

Using the quadratic equation root formula :

ax^2 + bx + c =0

x = ( -b + /- sqrt( b^2 -4ac)/2a

= ( - 3 + /- sqrt( 9 - 4*8*1)/2*1

= ( -3 + /- i*sqrt(23) )/2

= -3/2 + /- sqrt(23)/2

= a + bi

a = -3/2 ; b = sqrt(23)/2