6=x^2+8x+18

Solution for 6=x^2+8x+18 equation:

6=x^2+8x+18

We move all terms to the left:

6-(x^2+8x+18)=0

We get rid of parentheses

-x^2-8x-18+6=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 = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*-1}=\frac{12}{-2}
=-6
$