(3x-1)(9x+2)=0

Solution for (3x-1)(9x+2)=0 equation:

(3x-1)(9x+2)=0

We multiply parentheses ..

(+27x^2+6x-9x-2)=0

We get rid of parentheses

27x^2+6x-9x-2=0

We add all the numbers together, and all the variables

27x^2-3x-2=0

a = 27; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·27·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*27}=\frac{-12}{54}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*27}=\frac{18}{54}
=1/3
$