Y=-4.5x^2+5.5x+10

Solution for Y=-4.5x^2+5.5x+10 equation:

=-4.5Y^2+5.5Y+10

We move all terms to the left:

-(-4.5Y^2+5.5Y+10)=0

We get rid of parentheses

4.5Y^2-5.5Y-10=0

a = 4.5; b = -5.5; c = -10;
Δ = b2-4ac
Δ = -5.52-4·4.5·(-10)
Δ = 210.25
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{-(-5.5)-\sqrt{210.25}}{2*4.5}=\frac{5.5-\sqrt{210.25}}{9}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{210.25}}{2*4.5}=\frac{5.5+\sqrt{210.25}}{9}
$