Y=-4.5x^2+19x+300

Solution for Y=-4.5x^2+19x+300 equation:

=-4.5Y^2+19Y+300

We move all terms to the left:

-(-4.5Y^2+19Y+300)=0

We get rid of parentheses

4.5Y^2-19Y-300=0

a = 4.5; b = -19; c = -300;
Δ = b2-4ac
Δ = -192-4·4.5·(-300)
Δ = 5761
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{-(-19)-\sqrt{5761}}{2*4.5}=\frac{19-\sqrt{5761}}{9}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{5761}}{2*4.5}=\frac{19+\sqrt{5761}}{9}
$