Question

What are the solutions to 6X ^ 2 - 5x - 4 equals 0

Answer 1

x = -
`(1)/(2)`, x =
`(4)/(3)`

Explanation:

given 6x² - 5x - 4 = 0

Factorise by considering the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term, that is

product = 6 × - 4 = - 24 and sum = - 5

The factors are + 3 and - 8

Use these factors to split the middle term

6x² + 3x - 8x - 4 = 0 ( factor the first/second and third/fourth terms )

3x(2x + 1) - 4(2x + 1) = 0 ( take out common factor (2x + 1) )

(2x + 1)(3x - 4) = 0

equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
`(1)/(2)`

3x - 4 = 0 ⇒ 3x = 4 ⇒ x =
`(4)/(3)`

Answer 2

x=4/3, -2/1
hope this helps