20 pts

im checking my answer I think its one rational solution

Describe the number and type of solution of the following equation. 6x2 - 7x - 5 = 0

No solutions.

One rational solution.

Two rational solutions.

Two irrational solutions.

The answer to your question is Two rational solutions

Step-by-step explanation:

Quadratic equation

6x² - 7x - 5 = 0

Process

- Multiply 6 by - 5

6 x - 5 = - 30

- Find the prime factors of - 30

-30 2

-15 3

- 5 5

1

- Find to numbers that added gives - 7

this numbers are (2 x 5) = - 10 and + 3

- Write this numbers in the equation instead of - 7

6x² - 10x + 3x - 5

-Factor using like terms

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

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

- Equal to zero

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

x₁ = 5/3 x₂ = - 1/2

- Conclusion two rational solutions