(X-3)(x+4)-5x=0

Solution for (X-3)(x+4)-5x=0 equation:

(X-3)(X+4)-5X=0

We add all the numbers together, and all the variables

-5X+(X-3)(X+4)=0

We multiply parentheses ..

(+X^2+4X-3X-12)-5X=0

We get rid of parentheses

X^2+4X-3X-5X-12=0

We add all the numbers together, and all the variables

X^2-4X-12=0

a = 1; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*1}=\frac{12}{2}
=6
$