2=9x^2+6x+1

Solution for 2=9x^2+6x+1 equation:

2=9x^2+6x+1

We move all terms to the left:

2-(9x^2+6x+1)=0

We get rid of parentheses

-9x^2-6x-1+2=0

We add all the numbers together, and all the variables

-9x^2-6x+1=0

a = -9; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-9)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*-9}=\frac{6-6\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*-9}=\frac{6+6\sqrt{2}}{-18}
$