What is the root of the equation 6x^2-7x-5=0

The roots are {-1/2, 5/3}.

Step-by-step explanation:

6x^2 - 7x - 5 = 0

Use the 'ac' method:

6 * - 5 = - 30 so we need to find 2 values whose product is - 30 and whose sum = the coefficient of x in the given equation (-7).

-10 and + 3 fit the bill so we write:

6x^2 - 7x - 5 = 0

6x^2 + 3x - 10x - 5 = 0 Factor by grouping:

3x (2x + 1) - 5 (2x + 1) = 0

(3x - 5) (2x + 1) = 0

So 3x - 5 = 0 gives x = 5/3, and

2x + 1 = 0 gives x = - 1/2.