(x-2.5)(x-4.5)=0

Solution for (x-2.5)(x-4.5)=0 equation:

(x-2.5)(x-4.5)=0

We multiply parentheses ..

(+x^2-4.5x-2.5x+11.25)=0

We get rid of parentheses

x^2-4.5x-2.5x+11.25=0

We add all the numbers together, and all the variables

x^2-7x+11.25=0

a = 1; b = -7; c = +11.25;
Δ = b2-4ac
Δ = -72-4·1·11.25
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-2}{2*1}=\frac{5}{2}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+2}{2*1}=\frac{9}{2}
=4+1/2
$