solve 6x^2 - 17x + 12 = 0 for x using the quadratic formula
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 6, b = -17, and c = 12.
Substituting these values into the formula, we have:
x = (-(-17) ± √((-17)^2 - 4(6)(12))) / (2(6))
x = (17 ± √(289 - 288)) / 12
x = (17 ± √1) / 12
The square root of 1 is 1, so we have:
x = (17 + 1) / 12 = 18 / 12 = 3/2
x = (17 - 1) / 12 = 16 / 12 = 4/3
Therefore, the solutions for x are x = 3/2 and x = 4/3.