Simplify equation with square and non-square $y$

Question

I'm trying to solve a few equations but my math is a bit (very) rusty. In particular, I've simplified one of them to this:

$$2y^2-3y-2=0$$

I can see that the answer is "2" but how can I prove it? Is it possible to simplify the equation further?

Answer 1

Hint. You may use the formula for the roots of second degree polynomials. If you have a polynomial of degree two, say $ax^2 +bx+c$, the roots are given by $$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

Answer 2

You've stated an answer. There may be another distinct answer.

Pulling out the trusty quadratic formula:

$$y = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(-2)}}{2(2)}$$

$$y = \frac{3 \pm 5}{4}$$

$$y = 2 \text{ or } -1/2$$