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

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

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

We multiply parentheses ..

(+3x^2-27x+2x-18)=0

We get rid of parentheses

3x^2-27x+2x-18=0

We add all the numbers together, and all the variables

3x^2-25x-18=0

a = 3; b = -25; c = -18;
Δ = b2-4ac
Δ = -252-4·3·(-18)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-29}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+29}{2*3}=\frac{54}{6}
=9
$