0=-0.05x^2+4.5x-6.5

Solution for 0=-0.05x^2+4.5x-6.5 equation:

0=-0.05x^2+4.5x-6.5

We move all terms to the left:

0-(-0.05x^2+4.5x-6.5)=0

We add all the numbers together, and all the variables

-(-0.05x^2+4.5x-6.5)=0

We get rid of parentheses

0.05x^2-4.5x+6.5=0

a = 0.05; b = -4.5; c = +6.5;
Δ = b2-4ac
Δ = -4.52-4·0.05·6.5
Δ = 18.95
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{-(-4.5)-\sqrt{18.95}}{2*0.05}=\frac{4.5-\sqrt{18.95}}{0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{18.95}}{2*0.05}=\frac{4.5+\sqrt{18.95}}{0.1}
$