Use the quadratic formula to solve. Express your answer in simplest form.6, w, squared, plus, w, minus, 15, equals, 06w 2 +w−15=0

The quadratic formula is used to solve equations of the form ax^2 + bx + c = 0. The formula is given by:

x = [-b ± sqrt(b^2 - 4ac)] / (2a)

In this case, the equation is 6w^2 + w - 15 = 0. So, a = 6, b = 1, and c = -15.

First, calculate the value under the square root in the quadratic formula, which is b^2 - 4ac:

(1)^2 - 46(-15) = 1 + 360 = 361

The square root of 361 is 19.

Then, substitute a, b, and the square root value into the quadratic formula:

w = [-1 ± 19] / (2*6)

This gives two solutions:

w = (19 - 1) / 12 = 18 / 12 = 1.5

and

w = (-19 - 1) / 12 = -20 / 12 = -5/3

So, the solutions to the equation 6w^2 + w - 15 = 0 are w = 1.5 and w = -5/3.