0=18x^2-9x-1

Solution for 0=18x^2-9x-1 equation:

0=18x^2-9x-1

We move all terms to the left:

0-(18x^2-9x-1)=0

We add all the numbers together, and all the variables

-(18x^2-9x-1)=0

We get rid of parentheses

-18x^2+9x+1=0

a = -18; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-18)·1
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-18}=\frac{-9-3\sqrt{17}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-18}=\frac{-9+3\sqrt{17}}{-36}
$