Y=5.5-0.344x^2

Solution for Y=5.5-0.344x^2 equation:

=5.5-0.344Y^2

We move all terms to the left:

-(5.5-0.344Y^2)=0

We get rid of parentheses

0.344Y^2-5.5=0

a = 0.344; b = 0; c = -5.5;
Δ = b2-4ac
Δ = 02-4·0.344·(-5.5)
Δ = 7.568
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{-(0)-\sqrt{7.568}}{2*0.344}=\frac{0-\sqrt{7.568}}{0.688}
=-\frac{\sqrt{}}{0.688}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{7.568}}{2*0.344}=\frac{0+\sqrt{7.568}}{0.688}
=\frac{\sqrt{}}{0.688}
$