(x+3)(x-4)-x-x-6=0

Solution for (x+3)(x-4)-x-x-6=0 equation:

(x+3)(x-4)-x-x-6=0

We add all the numbers together, and all the variables

-2x+(x+3)(x-4)-6=0

We multiply parentheses ..

(+x^2-4x+3x-12)-2x-6=0

We get rid of parentheses

x^2-4x+3x-2x-12-6=0

We add all the numbers together, and all the variables

x^2-3x-18=0

a = 1; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·1·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*1}=\frac{12}{2}
=6
$