(x+6)(x-4)=24

Solution for (x+6)(x-4)=24 equation:

(x+6)(x-4)=24

We move all terms to the left:

(x+6)(x-4)-(24)=0

We multiply parentheses ..

(+x^2-4x+6x-24)-24=0

We get rid of parentheses

x^2-4x+6x-24-24=0

We add all the numbers together, and all the variables

x^2+2x-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$