x^2+6*3x+6=x

Solution for x^2+6*3x+6=x equation:

x^2+6*3x+6=x

We move all terms to the left:

x^2+6*3x+6-(x)=0

We add all the numbers together, and all the variables

x^2-1x+6*3x+6=0

Wy multiply elements

x^2-1x+18x+6=0

We add all the numbers together, and all the variables

x^2+17x+6=0

a = 1; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·1·6
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{265}}{2*1}=\frac{-17-\sqrt{265}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{265}}{2*1}=\frac{-17+\sqrt{265}}{2}
$