x*(2x+18)=0

Solution for x*(2x+18)=0 equation:

x(2x+18)=0

We multiply parentheses

2x^2+18x=0

a = 2; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·2·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*2}=\frac{0}{4}
=0
$