(x-3)(x-2)=12x+24

Solution for (x-3)(x-2)=12x+24 equation:

(x-3)(x-2)=12x+24

We move all terms to the left:

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

We get rid of parentheses

(x-3)(x-2)-12x-24=0

We multiply parentheses ..

(+x^2-2x-3x+6)-12x-24=0

We get rid of parentheses

x^2-2x-3x-12x+6-24=0

We add all the numbers together, and all the variables

x^2-17x-18=0

a = 1; b = -17; c = -18;
Δ = b2-4ac
Δ = -172-4·1·(-18)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*1}=\frac{36}{2}
=18
$