How Do You Solve This Quadratic Formula 6x^2+3x-18=0 Please Show The Work?

Divide both sides of the equation by 3.
  2x^2 + x - 6 = 0

This can be solved by factoring. We suspect that the factors of 2 (coefficient of x^2 term) and 6 (constant term) can be combined in a way that will give 1 (coefficient of x term).
  2x^2 + 4x - 3x - 6 = 0    (divide the x term into a sum of products)
  2x(x+2) - 3(x+2) = 0    (first factoring stage)
  (2x-3)(x+2) = 0    (second factoring stage)

Now, we have the factored equation. We can determine the roots by setting each of the factors to zero.
  2x-3 = 0
  x = 3/2

  x+2 = 0
  x = -2

The solutions are x = -2, x = 3/2.