(3x+2)(X-4)=24

Solution for (3x+2)(X-4)=24 equation:

(3x+2)(x-4)=24

We move all terms to the left:

(3x+2)(x-4)-(24)=0

We multiply parentheses ..

(+3x^2-12x+2x-8)-24=0

We get rid of parentheses

3x^2-12x+2x-8-24=0

We add all the numbers together, and all the variables

3x^2-10x-32=0

a = 3; b = -10; c = -32;
Δ = b2-4ac
Δ = -102-4·3·(-32)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*3}=\frac{32}{6}
=5+1/3
$