(3x+8)(x-6)=9x+24

Solution for (3x+8)(x-6)=9x+24 equation:

(3x+8)(x-6)=9x+24

We move all terms to the left:

(3x+8)(x-6)-(9x+24)=0

We get rid of parentheses

(3x+8)(x-6)-9x-24=0

We multiply parentheses ..

(+3x^2-18x+8x-48)-9x-24=0

We get rid of parentheses

3x^2-18x+8x-9x-48-24=0

We add all the numbers together, and all the variables

3x^2-19x-72=0

a = 3; b = -19; c = -72;
Δ = b2-4ac
Δ = -192-4·3·(-72)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-35}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+35}{2*3}=\frac{54}{6}
=9
$