Solution of this equation-stuck?

Question

Find all solutions of the equation and express them in the form a + bi.

a)x^2+(1/2)x+1=0
b)z+4+(12/z)=0

Any solutions or help is appreciated

Answer 1

a)

The solution of the equation in the form a + ib

x² + (1 / 2)x + 1 = 0

2x² + x + 2 = 0

This is a quadratic equation then the roots are x = (-b ±√(b² - 4ac)) / 2a

Substitute a = 2 , b = 1 and c = 2

                                                                                     x = [-1 ± √1 - 4(2)(2)] / 4

                                                                                      x = -1 ±√-15 / 4

                                                                                      x = (-1 ±i√15) / 4

                                                                                        x = -1 / 4 ±i√15 / 4

Answer 2

(b). The equation is z + 4 + (12/z) = 0.