(x+12)(x-4)=105

Solution for (x+12)(x-4)=105 equation:

(x+12)(x-4)=105

We move all terms to the left:

(x+12)(x-4)-(105)=0

We multiply parentheses ..

(+x^2-4x+12x-48)-105=0

We get rid of parentheses

x^2-4x+12x-48-105=0

We add all the numbers together, and all the variables

x^2+8x-153=0

a = 1; b = 8; c = -153;
Δ = b2-4ac
Δ = 82-4·1·(-153)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-26}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+26}{2*1}=\frac{18}{2}
=9
$