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

Solution for 0=9(x^2)-x-2 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-9x^2+x+2=0

a = -9; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-9)·2
Δ = 73
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{-(1)-\sqrt{73}}{2*-9}=\frac{-1-\sqrt{73}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*-9}=\frac{-1+\sqrt{73}}{-18}
$