(3x+2)(x-4)=9

Solution for (3x+2)(x-4)=9 equation:

(3x+2)(x-4)=9

We move all terms to the left:

(3x+2)(x-4)-(9)=0

We multiply parentheses ..

(+3x^2-12x+2x-8)-9=0

We get rid of parentheses

3x^2-12x+2x-8-9=0

We add all the numbers together, and all the variables

3x^2-10x-17=0

a = 3; b = -10; c = -17;
Δ = b2-4ac
Δ = -102-4·3·(-17)
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{19}}{2*3}=\frac{10-4\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{19}}{2*3}=\frac{10+4\sqrt{19}}{6}
$