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

Solution for (3x-6)(2x+9)=0 equation:

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

We multiply parentheses ..

(+6x^2+27x-12x-54)=0

We get rid of parentheses

6x^2+27x-12x-54=0

We add all the numbers together, and all the variables

6x^2+15x-54=0

a = 6; b = 15; c = -54;
Δ = b2-4ac
Δ = 152-4·6·(-54)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*6}=\frac{24}{12}
=2
$