Answer
{$-1,\frac{2}{5}$}
Work Step by Step
Step 1: Comparing $5x^{2}+3x-2=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=5$, $b=3$, and $c=-2$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a,b, and c in the formula, we obtain:
$x=\frac{-(3) \pm \sqrt {(3)^{2}-4(5)(-2)}}{2(5)}$
Step 4: $x=\frac{-3 \pm \sqrt {9+40}}{10}$
Step 5: $x=\frac{-3 \pm \sqrt {49}}{10}$
Step 6: $x=\frac{-3 \pm 7}{10}$
Step 7: $x=\frac{-3 + 7}{10}$ or $x=\frac{-3 - 7}{10}$
Step 8: $x=\frac{4}{10}$ or $x=\frac{-10}{10}$
Step 9: $x=\frac{2}{5}$ or $x=-1$
Step 10: Therefore, the solution set is {$-1,\frac{2}{5}$}.
