Answer
The solutions are $x=\dfrac{2}{3}\pm\dfrac{\sqrt{10}}{3}$
Work Step by Step
$(3x+2)(x-1)=3x$
Evaluate the product on the left side:
$3x^{2}-3x+2x-2=3x$
Take $3x$ to the left side and simplify:
$3x^{2}-3x+2x-3x-2=0$
$3x^{2}-4x-2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=3$, $b=-4$ and $c=−2$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-4)\pm\sqrt{(-4)^{2}-4(3)(-2)}}{2(3)}=\dfrac{4\pm\sqrt{16+24}}{6}=...$
$...=\dfrac{4\pm\sqrt{40}}{6}=\dfrac{4\pm2\sqrt{10}}{6}=\dfrac{4}{6}\pm\dfrac{2\sqrt{10}}{6}=\dfrac{2}{3}\pm\dfrac{\sqrt{10}}{3}$
The solutions are $x=\dfrac{2}{3}\pm\dfrac{\sqrt{10}}{3}$
