Solve 3x² − 4x − 2 = 0 using the quadratic formula.

1. 1 · Write what is given and what is to be found. 3x² − 4x − 2 = 0. To find: its roots.
2. 2 · Write the formula. x = (−b ± √(b² − 4ac))/(2a)
3. 3 · Identify a, b and c. a = 3, b = −4, c = −2
4. 4 · Find the discriminant. D = (−4)² − 4(3)(−2) = 16 + 24 = 40. D > 0, so there are two distinct real roots.
5. 5 · Substitute. x = (4 ± √40)/6 = (4 ± 2√10)/6
6. 6 · Simplify. Divide the top and bottom by 2: x = (2 + √10)/3 or x = (2 − √10)/3.
7. 7 · Check and box the answer. Sum = 4/3 = −b/a and product = (4 − 10)/9 = −2/3 = c/a. Therefore x = (2 ± √10)/3.

Scoring tip: Write the formula first, then a, b, c and D on separate lines. Each line can earn a method mark even if the last step slips.