Final answer:
To solve the equation 3c^2 + 14c - 8 = 4c using the quadratic formula, rearrange the equation in the form ax^2 + bx + c = 0. Substitute the values into the quadratic formula to find the solutions: c = 0 and c = -3.
Step-by-step explanation:
To solve the equation 3c^2 + 14c - 8 = 4c using the quadratic formula, we need to rearrange the equation in the form ax^2 + bx + c = 0. In this case, a = 3, b = 14 - 4 = 10, and c = -8. Substituting these values into the quadratic formula, we get:
c = (-b ± √(b^2 - 4ac))/(2a)
c = (-(14 - 4) ± √((14 - 4)^2 - 4(3)(-8)))/(2(3))
c = (-10 ± √(196 - 96))/(6)
c = (-10 ± √(100))/(6)
c = (-10 ± 10)/(6)
Therefore, the solutions are: c = 0 and c = -3.