-7x-6=x^2

Solution for -7x-6=x^2 equation:

-7x-6=x^2

We move all terms to the left:

-7x-6-(x^2)=0

determiningTheFunctionDomain
-x^2-7x-6=0

We add all the numbers together, and all the variables

-1x^2-7x-6=0

a = -1; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-1)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*-1}=\frac{12}{-2}
=-6
$