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

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

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

We multiply parentheses ..

(+6x^2-3x+18x-9)=0

We get rid of parentheses

6x^2-3x+18x-9=0

We add all the numbers together, and all the variables

6x^2+15x-9=0

a = 6; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·6·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*6}=\frac{6}{12}
=1/2
$