#### Answer

$x=5$

#### Work Step by Step

$\dfrac{2}{3}x^{2}-\dfrac{20}{3}x=-\dfrac{100}{6}$
Multiply the whole equation by $6$ to avoid working with fractions:
$6\Big(\dfrac{2}{3}x^{2}-\dfrac{20}{3}x=-\dfrac{100}{6}\Big)$
$4x^{2}-40x=-100$
Take all terms to the left side:
$4x^{2}-40x+100=0$
Take out common factor $4$ from the left side of the equation:
$4(x^{2}-10x+25)=0$
Take the common factor to multiply the right side of the equation. Since that side is $0$, the result is the expression inside the parentheses equal to $0$
$x^{2}-10x+25=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=1$, $b=-10$ and $c=25$
Substitute:
$x=\dfrac{-(-10)\pm\sqrt{(-10)^{2}-4(1)(25)}}{2(1)}=\dfrac{10\pm\sqrt{100-100}}{2}=...$
$...=\dfrac{10\pm\sqrt{0}}{2}=5$