-10x-21=x^2

Solution for -10x-21=x^2 equation:

-10x-21=x^2

We move all terms to the left:

-10x-21-(x^2)=0

determiningTheFunctionDomain
-x^2-10x-21=0

We add all the numbers together, and all the variables

-1x^2-10x-21=0

a = -1; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*-1}=\frac{6}{-2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*-1}=\frac{14}{-2}
=-7
$