Final answer:
To solve the quadratic equation 2x² − 3x + 6 = 0, we utilize the quadratic formula with a = 2, b = −3, and c = 6, and determine the two possible values for x, which may be complex if the discriminant is negative.
Step-by-step explanation:
To find the solutions for the quadratic equation 2x² − 3x + 6 = 0, we use the quadratic formula, which is x = −b ± √(b² − 4ac) / (2a).
For our equation, a = 2, b = −3, and c = 6. Plugging these values into the quadratic formula gives us:
x = (−3 ± √((-3)² − 4 × 2 × 6)) / (2 × 2).
Further simplification will yield the two possible values for x. However, it should be noted that if the value inside the square root (the discriminant) is negative, the solutions will be complex numbers.