0=-0.5x^2+5x-4.5

Solution for 0=-0.5x^2+5x-4.5 equation:

0=-0.5x^2+5x-4.5

We move all terms to the left:

0-(-0.5x^2+5x-4.5)=0

We add all the numbers together, and all the variables

-(-0.5x^2+5x-4.5)=0

We get rid of parentheses

0.5x^2-5x+4.5=0

a = 0.5; b = -5; c = +4.5;
Δ = b2-4ac
Δ = -52-4·0.5·4.5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-4}{2*0.5}=\frac{1}{1}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+4}{2*0.5}=\frac{9}{1}
=9
$