Y=9x^2-3x-2

Solution for Y=9x^2-3x-2 equation:

=9Y^2-3Y-2

We move all terms to the left:

-(9Y^2-3Y-2)=0

We get rid of parentheses

-9Y^2+3Y+2=0

a = -9; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-9)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-9}=\frac{-12}{-18}
=2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-9}=\frac{6}{-18}
=-1/3
$