Answer
{$-1.95,2.15$}
Work Step by Step
Step 1: Comparing $-5x^{2}+x+21=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain:
$a=-5$, $b=1$ and $c=21$
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:
$x=\frac{-(1) \pm \sqrt {(1)^{2}-4(-5)(21)}}{2(-5)}$
Step 4: $x=\frac{-1 \pm \sqrt {1+420}}{-10}$
Step 5: $x=\frac{-1 \pm \sqrt {421}}{-10}$
Step 6: $x=\frac{-1 \pm 20.518}{-10}$
Step 7: $x=\frac{-1 + 20.518}{-10}$ or $x=\frac{-1 - 20.518}{-10}$
Step 8: $x=\frac{19.518}{-10}$ or $x=\frac{-21.518}{-10}$
Step 9: $x=-1.9518\approx-1.95$ or $x=2.1518\approx2.15$
Step 10: Therefore, the solution set is {$-1.95,2.15$}.
