(-0.5*x^2)+(2.5*x)+(4.5)=0

Solution for (-0.5*x^2)+(2.5*x)+(4.5)=0 equation:

(-0.5x^2)+(2.5x)+(4.5)=0

We add all the numbers together, and all the variables

(-0.5x^2)+(+2.5x)+(4.5)=0

We add all the numbers together, and all the variables

(-0.5x^2)+(+2.5x)+4.5=0

We get rid of parentheses

-0.5x^2+2.5x+4.5=0

a = -0.5; b = 2.5; c = +4.5;
Δ = b2-4ac
Δ = 2.52-4·(-0.5)·4.5
Δ = 15.25
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{-(2.5)-\sqrt{15.25}}{2*-0.5}=\frac{-2.5-\sqrt{15.25}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{15.25}}{2*-0.5}=\frac{-2.5+\sqrt{15.25}}{-1}
$