Y=2x^2+9x+1

Solution for Y=2x^2+9x+1 equation:

=2Y^2+9Y+1

We move all terms to the left:

-(2Y^2+9Y+1)=0

We get rid of parentheses

-2Y^2-9Y-1=0

a = -2; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·(-2)·(-1)
Δ = 73
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{-(-9)-\sqrt{73}}{2*-2}=\frac{9-\sqrt{73}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{73}}{2*-2}=\frac{9+\sqrt{73}}{-4}
$