To solve for x in each quadratic equation, we can use the quadratic formula:

For the equation a) x² + 6x + 4 = 0
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a

Using the coefficients from equation a): a=1, b=6, c=4

x = (-6 ± √(6² - 414)) / 2*1
x = (-6 ± √(36 - 16)) / 2
x = (-6 ± √20) / 2
x = (-6 ± 2√5) / 2
x = -3 ± √5
So the solutions for equation a) are x = -3 + √5 and x = -3 - √5

For the equation b) x² + 106x + 693 = 0
Using the quadratic formula with coefficients a=1, b=106, c=693:

x = (-106 ± √(106² - 41693)) / 2*1
x = (-106 ± √(11236 - 2772)) / 2
x = (-106 ± √8464) / 2
x = (-106 ± 92) / 2
x = (-106 + 92) / 2 and x = (-106 - 92) / 2
x = -14 / 2 and x = -198 / 2
x = -7 and x = -99

So the solutions for equation b) are x = -7 and x = -99