0=-x^2+5.5x+3

Solution for 0=-x^2+5.5x+3 equation:

0=-x^2+5.5x+3

We move all terms to the left:

0-(-x^2+5.5x+3)=0

We add all the numbers together, and all the variables

-(-x^2+5.5x+3)=0

We get rid of parentheses

x^2-5.5x-3=0

a = 1; b = -5.5; c = -3;
Δ = b2-4ac
Δ = -5.52-4·1·(-3)
Δ = 42.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5.5)-\sqrt{42.25}}{2*1}=\frac{5.5-\sqrt{42.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{42.25}}{2*1}=\frac{5.5+\sqrt{42.25}}{2}
$