2(x+12)=x^2

Solution for 2(x+12)=x^2 equation:

2(x+12)=x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-x^2+2(x+12)=0

We add all the numbers together, and all the variables

-1x^2+2(x+12)=0

We multiply parentheses

-1x^2+2x+24=0

a = -1; b = 2; c = +24;
Δ = b2-4ac
Δ = 22-4·(-1)·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-1}=\frac{8}{-2}
=-4
$