Answer
$$x=\frac{\sqrt{19}-2}{5},\:x=\frac{-\sqrt{19}-2}{5}$$
Work Step by Step
In order to solve this problem, we use the method of completing the square. Doing this, we find:
$$ 5x^2+4x=3\\ x^2+\frac{4x}{5}+\left(\frac{2}{5}\right)^2=\frac{3}{5}+\left(\frac{2}{5}\right)^2\\ \left(x+\frac{2}{5}\right)^2=\frac{19}{25}\\ x=\frac{\sqrt{19}-2}{5},\:x=\frac{-\sqrt{19}-2}{5}$$
