Question

What are the solutoins to 6x^2-5x-4=0​

Answer 1

Answer:

see explanation

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the x- term

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

The factors are + 3 and - 8

Use these factors to split the x- term

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

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

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

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - $\frac{1}{2}$

3x - 4 = 0 ⇒ 3x = 4 ⇒ x = $\frac{4}{3}$

Solutions are x = - $\frac{1}{2}$, x = $\frac{4}{3}$