Final answer:
The solutions for the quadratic equation 3x² - 2x - 5 = 0 are found using the quadratic formula, which takes the form x = (-b ± √(b² - 4ac)) / (2a) when applied to any equation of the form ax² + bx + c = 0.
Step-by-step explanation:
The equation representing the solutions of the quadratic equation 3x² - 2x - 5 = 0 can be found by using the quadratic formula. The quadratic formula for an equation of the form ax² + bx + c = 0 is given by:
x = (-b ± √(b² - 4ac)) / (2a).
For the given equation, a=3, b=-2, and c=-5. Substituting these values into the quadratic formula, we get the solutions for x.