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

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

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

We multiply parentheses ..

(+27x^2+3x-27x-3)=0

We get rid of parentheses

27x^2+3x-27x-3=0

We add all the numbers together, and all the variables

27x^2-24x-3=0

a = 27; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·27·(-3)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-30}{2*27}=\frac{-6}{54}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+30}{2*27}=\frac{54}{54}
=1
$