Final answer:
To use the quadratic formula for the given quadratic equation, we rearrange it to the form ax² + bx + c = 0. Then, we identify the values of a, b, and c as 7, -6, and 1, respectively. Substituting these values into the quadratic formula gives us the solutions as (3 ± √2) / 7.
Step-by-step explanation:
In this case, the quadratic equation is given as 7x² = 6x - 1. To use the quadratic formula, we need to rearrange the equation in the form of ax² + bx + c = 0, where a, b, and c are constants. So, we have 7x² - 6x + 1 = 0.
Now, we can identify the values of a, b, and c. From the rearranged equation, a = 7, b = -6, and c = 1. Substituting these values into the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / (2a) = (-(-6) ± √((-6)² - 4(7)(1))) / (2(7)) = (6 ± √(36 - 28)) / 14 = (6 ± √8) / 14 = (6 ± √(4 × 2)) / 14 = (6 ± 2√2) / 14 = (3 ± √2) / 7.