Y=19x^2+50x+6

Solution for Y=19x^2+50x+6 equation:

=19Y^2+50Y+6

We move all terms to the left:

-(19Y^2+50Y+6)=0

We get rid of parentheses

-19Y^2-50Y-6=0

a = -19; b = -50; c = -6;
Δ = b2-4ac
Δ = -502-4·(-19)·(-6)
Δ = 2044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{511}}{2*-19}=\frac{50-2\sqrt{511}}{-38}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{511}}{2*-19}=\frac{50+2\sqrt{511}}{-38}
$