Y=-0.024x2+x+5.5

Solution for Y=-0.024x2+x+5.5 equation:

=-0.024Y^2+Y+5.5

We move all terms to the left:

-(-0.024Y^2+Y+5.5)=0

We get rid of parentheses

0.024Y^2-Y-5.5=0

We add all the numbers together, and all the variables

0.024Y^2-1Y-5.5=0

a = 0.024; b = -1; c = -5.5;
Δ = b2-4ac
Δ = -12-4·0.024·(-5.5)
Δ = 1.528
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{-(-1)-\sqrt{1.528}}{2*0.024}=\frac{1-\sqrt{1.528}}{0.048}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.528}}{2*0.024}=\frac{1+\sqrt{1.528}}{0.048}
$