Y=2x^2+17x+11

Solution for Y=2x^2+17x+11 equation:

=2Y^2+17Y+11

We move all terms to the left:

-(2Y^2+17Y+11)=0

We get rid of parentheses

-2Y^2-17Y-11=0

a = -2; b = -17; c = -11;
Δ = b2-4ac
Δ = -172-4·(-2)·(-11)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{201}}{2*-2}=\frac{17-\sqrt{201}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{201}}{2*-2}=\frac{17+\sqrt{201}}{-4}
$