What are the solutions to the quadratic equation 3x² + 14x + 16 = 0?

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Solutions to the Quadratic Equation

To find the solutions of the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula, which is given by:

x = (-b ± √(b² – 4ac)) / (2a)

In this equation, the coefficients are:

  • a = 3
  • b = 14
  • c = 16

Now, let’s calculate the discriminant (b² – 4ac):

  • Discriminant = (14)² – 4(3)(16)
  • Discriminant = 196 – 192
  • Discriminant = 4

Since the discriminant is positive, we will have two distinct real solutions. Now, substituting the values into the quadratic formula:

  • x = (-14 ± √4) / (2 * 3)
  • x = (-14 ± 2) / 6

Now, we solve for the two possible values of x:

  1. First solution:
    • x = (-14 + 2) / 6
    • x = -12 / 6
    • x = -2
  2. Second solution:
    • x = (-14 – 2) / 6
    • x = -16 / 6
    • x = -8/3

Final Solutions:

  • x = -2
  • x = -8/3

Conclusion: The solutions to the equation 3x² + 14x + 16 = 0 are x = -2 and x = -8/3.

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