Find the solution for the following quadratic equations: a) 3x^2 + 9x - 27 = 0 b) x^2 + 2x - 15 = 0

a) 3x^2 + 9x - 27 = 0 

First let us
divide by 3 to simplify the equation:

==> x^2 + 3x - 9) =
0

Now we will use the formula to
solve.

We know that:

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

Let us
substitute.

x1 = ( -3 + sqrt(9 -4*-9) / 2 = ( -3 +
sqrt(45)/2

==> x1 =
(-3+3sqrt5)/2

==>x2=
(-3-3sqrt5)/2

 b) x^2 + 2x - 15 =
0

To solve the equation we will use the factoring
method.

First, we will factor the
equation.

==> ( x+5) ( x-3) =
0

==> x1=
-5

==> x2=
3

==> x values are { -5,
3}