Solve 6k^2-17k-3=0
6 * 3 = 18 - 1 = 17
Adjust positives and negatives.
-k + -5k – -8k – 17k = -15
To solve the quadratic equation 6k^2 - 17k - 3 = 0, we can use the quadratic formula.
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions (roots) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation 6k^2 - 17k - 3 = 0, we have:
a = 6
b = -17
c = -3
Substituting these values into the quadratic formula, we have:
k = (-(-17) ± √((-17)^2 - 4 * 6 * (-3))) / (2 * 6)
Simplifying further:
k = (17 ± √(289 + 72)) / 12
k = (17 ± √(361)) / 12
k = (17 ± 19) / 12
Now, we have two possibilities:
1. k = (17 + 19) / 12 = 36 / 12 = 3
2. k = (17 - 19) / 12 = -2 / 12 = -1/6
So the solutions to the quadratic equation 6k^2 - 17k - 3 = 0 are k = 3 and k = -1/6.