-12=6x+x^2-42

Solution for -12=6x+x^2-42 equation:

-12=6x+x^2-42

We move all terms to the left:

-12-(6x+x^2-42)=0

We get rid of parentheses

-x^2-6x+42-12=0

We add all the numbers together, and all the variables

-1x^2-6x+30=0

a = -1; b = -6; c = +30;
Δ = b2-4ac
Δ = -62-4·(-1)·30
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-1}=\frac{6-2\sqrt{39}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-1}=\frac{6+2\sqrt{39}}{-2}
$