78=6x+6+x^2

Solution for 78=6x+6+x^2 equation:

78=6x+6+x^2

We move all terms to the left:

78-(6x+6+x^2)=0

We get rid of parentheses

-x^2-6x-6+78=0

We add all the numbers together, and all the variables

-1x^2-6x+72=0

a = -1; b = -6; c = +72;
Δ = b2-4ac
Δ = -62-4·(-1)·72
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-1}=\frac{24}{-2}
=-12
$