x(x+3)-18(x+3)=0

Solution for x(x+3)-18(x+3)=0 equation:

x(x+3)-18(x+3)=0

We multiply parentheses

x^2+3x-18x-54=0

We add all the numbers together, and all the variables

x^2-15x-54=0

a = 1; b = -15; c = -54;
Δ = b2-4ac
Δ = -152-4·1·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*1}=\frac{36}{2}
=18
$