Final answer:
To solve the equation 2x² - 3x - 7 = 0 using the quadratic formula, substitute the values of a = 2, b = -3, and c = -7 into the formula: x = (-b ± √(b² - 4ac)) / (2a). Calculate the square root and perform the arithmetic to get the values of x.
Step-by-step explanation:
To solve the equation 2x² - 3x - 7 = 0 using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = 2, b = -3, and c = -7. Now, we can substitute these values into the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-(-3) ± √((-3)² - 4(2)(-7))) / (2(2))
x = (3 ± √(9 + 56)) / 4
x = (3 ± √65) / 4
Therefore, the values of x are (3 + √65) / 4 and (3 - √65) / 4.