Y=9x^2-18x-7

Solution for Y=9x^2-18x-7 equation:

=9Y^2-18Y-7

We move all terms to the left:

-(9Y^2-18Y-7)=0

We get rid of parentheses

-9Y^2+18Y+7=0

a = -9; b = 18; c = +7;
Δ = b2-4ac
Δ = 182-4·(-9)·7
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*-9}=\frac{-42}{-18}
=2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*-9}=\frac{6}{-18}
=-1/3
$