Use the quadratic formula to solve. Express your answer in simplest form.6, b, squared, minus, 7, b, minus, 21, equals, minus, 16b 2 −7b−21=−1

The given equation is 6b^2 - 7b - 21 = -16b.

First, let's simplify the equation by adding 16b to both sides to set the equation to equal zero. This gives us:

6b^2 - 7b + 16b - 21 = 0

Simplify further to:

6b^2 + 9b - 21 = 0

Now we can use the quadratic formula to solve for b. The quadratic formula is:

b = [-B ± sqrt(B^2 - 4AC)] / 2A

In our equation, A = 6, B = 9, and C = -21.

Substitute A, B, and C into the formula:

b = [-9 ± sqrt((9)^2 - 46(-21))] / 2*6 b = [-9 ± sqrt(81 + 504)] / 12 b = [-9 ± sqrt(585)] / 12

Simplify the square root:

b = [-9 ± 3*sqrt(65)] / 12

Divide each term in the numerator by the denominator:

b = -3/4 ± sqrt(65)/4

So, the solutions to the equation are b = -3/4 + sqrt(65)/4 and b = -3/4 - sqrt(65)/4.