Y=2x^2+13x+19

Solution for Y=2x^2+13x+19 equation:

=2Y^2+13Y+19

We move all terms to the left:

-(2Y^2+13Y+19)=0

We get rid of parentheses

-2Y^2-13Y-19=0

a = -2; b = -13; c = -19;
Δ = b2-4ac
Δ = -132-4·(-2)·(-19)
Δ = 17
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{-(-13)-\sqrt{17}}{2*-2}=\frac{13-\sqrt{17}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{17}}{2*-2}=\frac{13+\sqrt{17}}{-4}
$