**Finding B in the Quadratic Equation B^2 + 3B - 15 = 0**

To find the value of B in the given quadratic equation B^2 + 3B - 15 = 0, we will use the quadratic formula. The quadratic formula gives the solutions for any quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients.

**Quadratic Formula:**

The quadratic formula states that for any quadratic equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In our given equation B^2 + 3B - 15 = 0, we can see that the coefficient of B^2 is 1 (a = 1), the coefficient of B is 3 (b = 3), and the constant term is -15 (c = -15). By substituting these values into the quadratic formula, we can find the solutions for B.

**Substituting values into the Quadratic Formula:**

Using the quadratic formula, we substitute the values of a, b, and c into the formula to find the solutions for B:

B = (-3 ± √(3^2 - 4 * 1 * -15)) / 2 * 1

Simplifying further:

B = (-3 ± √(9 + 60)) / 2

B = (-3 ± √69) / 2

**Calculating the Solutions:**

Now, we have two possible solutions for B obtained by using the ± symbol in the quadratic formula:

1. B = (-3 + √69) / 2
2. B = (-3 - √69) / 2

These are the two possible values of B that satisfy the given quadratic equation B^2 + 3B - 15 = 0.

**Conclusion:**

In conclusion, by applying the quadratic formula, we found that the values of B that satisfy the equation B^2 + 3B - 15 = 0 are B = (-3 + √69) / 2 and B = (-3 - √69) / 2. These solutions can be further simplified if necessary.