(3x-6)(9x+4)=0

Solution for (3x-6)(9x+4)=0 equation:

(3x-6)(9x+4)=0

We multiply parentheses ..

(+27x^2+12x-54x-24)=0

We get rid of parentheses

27x^2+12x-54x-24=0

We add all the numbers together, and all the variables

27x^2-42x-24=0

a = 27; b = -42; c = -24;
Δ = b2-4ac
Δ = -422-4·27·(-24)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-66}{2*27}=\frac{-24}{54}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+66}{2*27}=\frac{108}{54}
=2
$