(6x+3)(3x-9)=0

Solution for (6x+3)(3x-9)=0 equation:

(6x+3)(3x-9)=0

We multiply parentheses ..

(+18x^2-54x+9x-27)=0

We get rid of parentheses

18x^2-54x+9x-27=0

We add all the numbers together, and all the variables

18x^2-45x-27=0

a = 18; b = -45; c = -27;
Δ = b2-4ac
Δ = -452-4·18·(-27)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-63}{2*18}=\frac{-18}{36}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+63}{2*18}=\frac{108}{36}
=3
$