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

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

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

We multiply parentheses ..

(+27x^2+12x-81x-36)=0

We get rid of parentheses

27x^2+12x-81x-36=0

We add all the numbers together, and all the variables

27x^2-69x-36=0

a = 27; b = -69; c = -36;
Δ = b2-4ac
Δ = -692-4·27·(-36)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-93}{2*27}=\frac{-24}{54}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+93}{2*27}=\frac{162}{54}
=3
$