Y=0.0241x2+x+5.5

Solution for Y=0.0241x2+x+5.5 equation:

=0.0241Y^2+Y+5.5

We move all terms to the left:

-(0.0241Y^2+Y+5.5)=0

We get rid of parentheses

-0.0241Y^2-Y-5.5=0

We add all the numbers together, and all the variables

-0.0241Y^2-1Y-5.5=0

a = -0.0241; b = -1; c = -5.5;
Δ = b2-4ac
Δ = -12-4·(-0.0241)·(-5.5)
Δ = 0.4698
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{0.4698}}{2*-0.0241}=\frac{1-\sqrt{0.4698}}{-0.0482}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.4698}}{2*-0.0241}=\frac{1+\sqrt{0.4698}}{-0.0482}
$