Answer
$\{4,\frac{-2}{3}\}$
Work Step by Step
$3x^{2}-10x=8$
Dividing both sides by $3$
$x^{2}-\frac{10}{3}x=\frac{8}{3}$
Adding the square of half the co-efficient of $x$ to both sides,
$x^{2}-\frac{10}{3}x+\frac{25}{9}=\frac{8}{3}+\frac{25}{9}$
$(x-\frac{5}{3})^{2}=\frac{24+25}{9}$
$(x-\frac{5}{3})^{2}=\frac{49}{9}$
$(x-\frac{5}{3})=±\sqrt (\frac{49}{9})$
$x-\frac{5}{3}=±\frac{7}{3}$
$x=\frac{5}{3}±\frac{7}{3}$
$x=\frac{5}{3}+\frac{7}{3}$ or $x=\frac{5}{3}-\frac{7}{3}$
$x=\frac{12}{3}$ or $x=\frac{-2}{3}$
$x=4$ or $x=\frac{-2}{3}$
