Answer
$\displaystyle x=\frac{5\pm\sqrt{37}}{6}$
Work Step by Step
$\displaystyle \frac{3}{5}x^{2}-x=\frac{1}{5}$
We multiply by $5$:
$5(\displaystyle \frac{3}{5}x^{2}-x)=5*\frac{1}{5}$
$3x^{2}-5x=1$
$3x^{2}-5x-1=0$
We solve using the quadratic formula ($a=3,\ b=-5,\ c=-1$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-(-5)\pm\sqrt{(-5)^{2}-4*3*-1}}{2*3}$
$\displaystyle x=\frac{5\pm\sqrt{25+12}}{6}$
$\displaystyle x=\frac{5\pm\sqrt{37}}{6}$
