Solve for x 6x^2-2x-4=0

Problem

6*x2−2*x−4=0

Solution

1. Divide the entire equation by the greatest common factor, which is 2 to simplify the coefficients.

3*x2−x−2=0

2. Identify the coefficients a b and c for the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

a=3

b=−1

c=−2

3. Substitute the values into the quadratic formula.

x=(−(−1)±√(,(−1)2−4*(3)*(−2)))/(2*(3))

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

x=(1±√(,1+24))/6

x=(1±√(,25))/6

5. Evaluate the square root and solve for both possible values of x

x=(1±5)/6

6. Calculate the first solution using the plus sign.

x=(1+5)/6=6/6=1

7. Calculate the second solution using the minus sign.

x=(1−5)/6=(−4)/6=−2/3

Final Answer

x=1,−2/3

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