Solve for x 9x^2-6x-3=0

Problem

9*x2−6*x−3=0

Solution

1. Divide the entire equation by the greatest common factor, which is 3 to simplify the coefficients.

3*x2−2*x−1=0

2. Identify the coefficients for the quadratic formula a*x2+b*x+c=0 where a=3 b=−2 and c=−1

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the quadratic formula.

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

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

x=(2±√(,4+12))/6

x=(2±√(,16))/6

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

x=(2±4)/6

6. Calculate the first solution using the plus sign.

x=(2+4)/6=6/6=1

7. Calculate the second solution using the minus sign.

x=(2−4)/6=(−2)/6=−1/3

Final Answer

x=1,−1/3

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