Answer
$\displaystyle x=\frac{3\pm\sqrt{29}}{10}$
Work Step by Step
$\displaystyle \frac{5}{3}x^{2}-x=\frac{1}{3}$
We multiply by $3$:
$3(\displaystyle \frac{5}{3}x^{2}-x)=3*\frac{1}{3}$
$5x^{2}-3x=1$
$5x^{2}-3x-1=0$
We solve using the quadratic formula ($a=5,\ b=-3,\ c=-1$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-(-3)\pm\sqrt{(-3)^{2}-4*5*-1}}{2*5}$
$\displaystyle x=\frac{3\pm\sqrt{9+20}}{10}$
$\displaystyle x=\frac{3\pm\sqrt{29}}{10}$
