-12x-5=x^2

Solution for -12x-5=x^2 equation:

-12x-5=x^2

We move all terms to the left:

-12x-5-(x^2)=0

determiningTheFunctionDomain
-x^2-12x-5=0

We add all the numbers together, and all the variables

-1x^2-12x-5=0

a = -1; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·(-1)·(-5)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{31}}{2*-1}=\frac{12-2\sqrt{31}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{31}}{2*-1}=\frac{12+2\sqrt{31}}{-2}
$