Y=-4.5x^2-27x+48.5

Solution for Y=-4.5x^2-27x+48.5 equation:

=-4.5Y^2-27Y+48.5

We move all terms to the left:

-(-4.5Y^2-27Y+48.5)=0

We get rid of parentheses

4.5Y^2+27Y-48.5=0

a = 4.5; b = 27; c = -48.5;
Δ = b2-4ac
Δ = 272-4·4.5·(-48.5)
Δ = 1602
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:

$\sqrt{\Delta}=\sqrt{1602}=\sqrt{9*178}=\sqrt{9}*\sqrt{178}=3\sqrt{178}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{178}}{2*4.5}=\frac{-27-3\sqrt{178}}{9}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{178}}{2*4.5}=\frac{-27+3\sqrt{178}}{9}
$