Y=2x^2-9x-11

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

=2Y^2-9Y-11

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = 9; c = +11;
Δ = b2-4ac
Δ = 92-4·(-2)·11
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-13}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+13}{2*-2}=\frac{4}{-4}
=-1
$