-12x-5=x^2

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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} $

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