Y=-0,055x2+x+5,10

Solution for Y=-0,055x2+x+5,10 equation:

=-0.055Y^2+Y+5.10

We move all terms to the left:

-(-0.055Y^2+Y+5.10)=0

We get rid of parentheses

0.055Y^2-Y-5.10=0

We add all the numbers together, and all the variables

0.055Y^2-1Y-5.1=0

a = 0.055; b = -1; c = -5.1;
Δ = b2-4ac
Δ = -12-4·0.055·(-5.1)
Δ = 2.122
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{2.122}}{2*0.055}=\frac{1-\sqrt{2.122}}{0.11}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2.122}}{2*0.055}=\frac{1+\sqrt{2.122}}{0.11}
$