Answer
$7, -3$
Work Step by Step
For the equation $x^2 -4x -21= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=1, \quad b=-4, \quad c=-21
.$$
That is, $$ x=\frac{4 \pm \sqrt{16+84}}{2 }=\frac{4 \pm10}{2 }= 7, \ or, \ -3
.$$
Check the result:
$$
7^2-28-21=21-21=0, \quad
3^2+12-21=21-21=0.
$$
