10. solve the equation below using the quadratic formula.\n6x² - 17x + 12 = 0

Explanation:

Step1: Identify coefficients

For the quadratic equation (ax^{2}+bx + c = 0), here (a = 6), (b=-17), (c = 12).

Step2: Calculate discriminant

The discriminant (\Delta=b^{2}-4ac). Substitute (a = 6), (b=-17), (c = 12) into it: (\Delta=(-17)^{2}-4\times6\times12) (=289 - 288) (=1)

Step3: Apply quadratic formula

The quadratic formula is (x=\frac{-b\pm\sqrt{\Delta}}{2a}). Substitute (a = 6), (b=-17), (\Delta = 1) into it: (x=\frac{-(-17)\pm\sqrt{1}}{2\times6}=\frac{17\pm1}{12}) When take the plus sign: (x_{1}=\frac{17 + 1}{12}=\frac{18}{12}=\frac{3}{2}) When take the minus sign: (x_{2}=\frac{17-1}{12}=\frac{16}{12}=\frac{4}{3})

Answer:

(x=\frac{3}{2}) or (x=\frac{4}{3})