Solve Using the Quadratic Formula 3x^2-2x-8=0

Problem

3*x2−2*x−8=0

Solution

1. Identify the coefficients a b and c from the standard form a*x2+b*x+c=0

a=3

b=−2

c=−8

2. Apply the quadratic formula by substituting the identified values into the formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−2)±√(,(−2)2−4*(3)*(−8)))/(2*(3))

3. Simplify the expression inside the square root (the discriminant).

x=(2±√(,4+96))/6

x=(2±√(,100))/6

4. Evaluate the square root and solve for the two possible values of x

x=(2±10)/6

5. Calculate the first solution using the plus sign.

x=(2+10)/6

x=12/6

x=2

6. Calculate the second solution using the minus sign.

x=(2−10)/6

x=(−8)/6

x=−4/3

Final Answer

x=2,−4/3

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