b. 3t2 + 24t + 45 = 0

To solve the quadratic equation 3t^2 + 24t + 45 = 0, we can follow these steps:

Step 1: Identify the coefficients a, b, and c in the equation. In this case, a = 3, b = 24, and c = 45.

Step 2: Calculate the discriminant using the formula D = b^2 - 4ac. Here, D = (24)^2 - 4345 = 576 - 540 = 36.

Step 3: Use the quadratic formula to find the solutions. The quadratic formula is t = [-b ± sqrt(D)] / (2a).

So, the solutions are:

t1 = [ -24 + sqrt(36) ] / (23) = -4 t2 = [ -24 - sqrt(36) ] / (23) = -5

So, the solutions to the equation 3t^2 + 24t + 45 = 0 are t = -4 and t = -5.

To solve the quadratic equation 3t^2 + 24t + 45 = 0, we can use the quadratic formula, which is given by:

t = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, a = 3, b = 24, and c = 45.

Step 1: Calculate the discriminant (b^2 - 4ac)

Discriminant = (24)^2 - 4345 = 576 - 540 = 36

Step 2: Substitute a, b, and the discriminant into the quadratic formula

t = [-24 ± sqrt(36)] / (2*3) t = [-24 ± 6] / 6

Step 3: Solve for t

t = -30/6 or t = -18/6 t = -5 or t = -3

So, the solutions to the equation 3t^2 + 24t + 45 = 0 are t = -5 and t = -3.