Answer
$$x=\frac{\sqrt{37}+5}{6},\:x=\frac{-\sqrt{37}+5}{6}$$
Work Step by Step
To find the x-intercepts, we set the equation equal to zero and then complete the square. Doing this, we find:
$$ 3x^2-5x-1=0 \\ x^2-\frac{5x}{3}=\frac{1}{3}\\ x^2-\frac{5x}{3}+\left(-\frac{5}{6}\right)^2=\frac{1}{3}+\left(-\frac{5}{6}\right)^2\\ \left(x-\frac{5}{6}\right)^2=\frac{37}{36}\\ x=\frac{\sqrt{37}+5}{6},\:x=\frac{-\sqrt{37}+5}{6}$$
