0=18x^2+9x-2

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

0=18x^2+9x-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -18; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-18)·2
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-18}=\frac{-6}{-36}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-18}=\frac{24}{-36}
=-2/3
$