Y=-19+28x-7x^2

Solution for Y=-19+28x-7x^2 equation:

=-19+28Y-7Y^2

We move all terms to the left:

-(-19+28Y-7Y^2)=0

We get rid of parentheses

7Y^2-28Y+19=0

a = 7; b = -28; c = +19;
Δ = b2-4ac
Δ = -282-4·7·19
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-6\sqrt{7}}{2*7}=\frac{28-6\sqrt{7}}{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+6\sqrt{7}}{2*7}=\frac{28+6\sqrt{7}}{14}
$