12+8x=x^2

Solution for 12+8x=x^2 equation:

12+8x=x^2

We move all terms to the left:

12+8x-(x^2)=0

determiningTheFunctionDomain
-x^2+8x+12=0

We add all the numbers together, and all the variables

-1x^2+8x+12=0

a = -1; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-1)·12
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-1}=\frac{-8-4\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-1}=\frac{-8+4\sqrt{7}}{-2}
$