0=x(x-4.5)

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

0=x(x-4.5)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(x-4.5))=0


We calculate terms in parentheses: -(x(x-4.5)), so:

x(x-4.5)

We multiply parentheses

x^2-4.5x

Back to the equation:

-(x^2-4.5x)


We get rid of parentheses

-x^2+4.5x=0

We add all the numbers together, and all the variables

-1x^2+4.5x=0

a = -1; b = 4.5; c = 0;
Δ = b2-4ac
Δ = 4.52-4·(-1)·0
Δ = 20.25
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{-(4.5)-\sqrt{20.25}}{2*-1}=\frac{-4.5-\sqrt{20.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{20.25}}{2*-1}=\frac{-4.5+\sqrt{20.25}}{-2}
$