3(3x+1)(9x-12)=0

Solution for 3(3x+1)(9x-12)=0 equation:

3(3x+1)(9x-12)=0

We multiply parentheses ..

3(+27x^2-36x+9x-12)=0

We multiply parentheses

81x^2-108x+27x-36=0

We add all the numbers together, and all the variables

81x^2-81x-36=0

a = 81; b = -81; c = -36;
Δ = b2-4ac
Δ = -812-4·81·(-36)
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-135}{2*81}=\frac{-54}{162}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+135}{2*81}=\frac{216}{162}
=1+1/3
$