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

Solution for 0=(6x^2)+9x+1 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -6; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·(-6)·(-1)
Δ = 57
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{-(-9)-\sqrt{57}}{2*-6}=\frac{9-\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*-6}=\frac{9+\sqrt{57}}{-12}
$