I need help with these problems please:

Solve by Factoring:

$\displaystyle 3x^2 + 6x - 24 = 0$

The problem i got is that any combination of number I got that produced -24 didn't add to 6.

Mr F says: Start by writing it as 3(x^2 + 2x - 8) = 0.
And:

$\displaystyle 5x^2 - 40x - 45 = 0$

Mr F says: Start by writing it as 5(x^2 - 8x - 9) = 0.
And:

$\displaystyle 9x^2 + 24x + 16$

Mr F says: This has the form of a perfect square.
Solve the equation.

$\displaystyle 4x^2 + 9 = 0$

Mr F says: $\displaystyle {\color{red}x^2 = -\frac{9}{4} \Rightarrow x = \sqrt{-\frac{9}{4}} = \pm i \, \frac{3}{2}}$.
The answers were:

a. $\displaystyle \frac{-3}{2}i, \frac{3}{2}i $ b. $\displaystyle \frac{-9}{4}i , \frac{9}{4}i$

Use the Quadratic Formula to solve the equation.

$\displaystyle -2x^2 - 5x + 3 = 0$

My solution didn't match the 2 possible answers provided:

$\displaystyle \frac{-27}{2} , 11 $ and $\displaystyle -3 , \frac{1}{2} $

Mr F says: Show your working.
$\displaystyle 4x^2 - x + 9 = 0$

provided possible answers:

$\displaystyle \frac{1}{4} +- \frac{i\sqrt143}{4}$ or $\displaystyle \frac{1}{8} +- \frac{i\sqrt143}{8}$

Mr F says: Show your working.
I know its kind of alot but I absolutely cannot figure this out! Help is very appreciated