Y=9x^2+11x-14

Solution for Y=9x^2+11x-14 equation:

=9Y^2+11Y-14

We move all terms to the left:

-(9Y^2+11Y-14)=0

We get rid of parentheses

-9Y^2-11Y+14=0

a = -9; b = -11; c = +14;
Δ = b2-4ac
Δ = -112-4·(-9)·14
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*-9}=\frac{-14}{-18}
=7/9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*-9}=\frac{36}{-18}
=-2
$