Use the quadratic formula to solve. Express your answer in simplest form.4, d, squared, minus, 5, d, minus, 5, equals, 3, d4d 2 −5d−5=3d

First, let's rewrite the equation in standard form (ax^2 + bx + c = 0). The equation given is 4d^2 - 5d - 5 = 3d. We can subtract 3d from both sides to get it in standard form:

4d^2 - 8d - 5 = 0

Now we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this case, a = 4, b = -8, and c = -5.

So, we plug these values into the quadratic formula:

d = [8 ± sqrt((-8)^2 - 44(-5))] / (2*4) d = [8 ± sqrt(64 + 80)] / 8 d = [8 ± sqrt(144)] / 8 d = [8 ± 12] / 8

This gives us two solutions:

d = 20 / 8 = 2.5 d = -4 / 8 = -0.5

So, the solutions to the equation 4d^2 - 8d - 5 = 0 are d = 2.5 and d = -0.5.