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

Solution for 12x+12-x^2+1=8x-8 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2+12x-(8x-8)+13=0

We get rid of parentheses

-1x^2+12x-8x+8+13=0

We add all the numbers together, and all the variables

-1x^2+4x+21=0

a = -1; b = 4; c = +21;
Δ = b2-4ac
Δ = 42-4·(-1)·21
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{-(4)-10}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*-1}=\frac{6}{-2}
=-3
$