We are asked to solve the following quadratic equations: 5) $6m^2 + 12m - 48 = 0$ 6) $3x^2 - 15x - 18 = 0$ 7) $p^2 - 15 = -2p$ 8) $-4b^2 + 9b + 8 = -5b^2$

1. Problem Description

We are asked to solve the following quadratic equations:

5) $6m^2 + 12m - 48 = 0$

6) $3x^2 - 15x - 18 = 0$

7) $p^2 - 15 = -2p$

8) $-4b^2 + 9b + 8 = -5b^2$

2. Solution Steps

5) $6m^2 + 12m - 48 = 0$

First, divide the equation by 6:

$m^2 + 2m - 8 = 0$

Now, factor the quadratic equation:

$(m + 4)(m - 2) = 0$

Therefore, $m + 4 = 0$ or $m - 2 = 0$

$m = -4$ or $m = 2$

6) $3x^2 - 15x - 18 = 0$

First, divide the equation by 3:

$x^2 - 5x - 6 = 0$

Now, factor the quadratic equation:

$(x - 6)(x + 1) = 0$

Therefore, $x - 6 = 0$ or $x + 1 = 0$

$x = 6$ or $x = -1$

7) $p^2 - 15 = -2p$

First, rewrite the equation:

$p^2 + 2p - 15 = 0$

Now, factor the quadratic equation:

$(p + 5)(p - 3) = 0$

Therefore, $p + 5 = 0$ or $p - 3 = 0$

$p = -5$ or $p = 3$

8) $-4b^2 + 9b + 8 = -5b^2$

First, rewrite the equation:

$-4b^2 + 5b^2 + 9b + 8 = 0$

$b^2 + 9b + 8 = 0$

Now, factor the quadratic equation:

$(b + 8)(b + 1) = 0$

Therefore, $b + 8 = 0$ or $b + 1 = 0$

$b = -8$ or $b = -1$

3. Final Answer

5) $m = -4, 2$

6) $x = -1, 6$

7) $p = -5, 3$

8) $b = -8, -1$