Answer
$ \frac{2 ± \sqrt 10}{3}$
Work Step by Step
The trinomial cannot be factored so we use the quadratic formula to calculate the x.
$x= \frac{-b ± \sqrt (b^{2} - 4ac)}{2a}$
$3y^{2} - 4y - 2$
In this trinomial a = 3, b= -4 and c= -2
$x= \frac{-(-4) ± \sqrt (-4^{2} - 4(3)(-2))}{2(3)}$
$x= \frac{4 ± \sqrt (16 + 24)}{6}$
We add the 16 and 24 together
$x= \frac{4 ± \sqrt (40)}{6}$
Square root of 40 is $2\sqrt 10$ because the factors of 10 are 4 and 5; and 4 is a perfect square of 2.
$x= \frac{4 ± 2\sqrt 10}{6}$
We simplify the numbers to get the final x value.
$x= \frac{2 ± \sqrt 10}{3}$
