x(x+4.5)=0

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

x(x+4.5)=0

We multiply parentheses

x^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}
$