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

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

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

We multiply parentheses ..

(+9x^2-18x+6x-12)=0

We get rid of parentheses

9x^2-18x+6x-12=0

We add all the numbers together, and all the variables

9x^2-12x-12=0

a = 9; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·9·(-12)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*9}=\frac{36}{18}
=2
$