1=x+6x+9x^2

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

1=x+6x+9x^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-9x^2-7x+1=0

a = -9; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·(-9)·1
Δ = 85
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{-(-7)-\sqrt{85}}{2*-9}=\frac{7-\sqrt{85}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{85}}{2*-9}=\frac{7+\sqrt{85}}{-18}
$