(2x-4)(x+6)=24(39)

Solution for (2x-4)(x+6)=24(39) equation:

(2x-4)(x+6)=24(39)

We move all terms to the left:

(2x-4)(x+6)-(24(39))=0

determiningTheFunctionDomain
(2x-4)(x+6)-2439=0

We multiply parentheses ..

(+2x^2+12x-4x-24)-2439=0

We get rid of parentheses

2x^2+12x-4x-24-2439=0

We add all the numbers together, and all the variables

2x^2+8x-2463=0

a = 2; b = 8; c = -2463;
Δ = b2-4ac
Δ = 82-4·2·(-2463)
Δ = 19768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19768}=\sqrt{4*4942}=\sqrt{4}*\sqrt{4942}=2\sqrt{4942}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{4942}}{2*2}=\frac{-8-2\sqrt{4942}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{4942}}{2*2}=\frac{-8+2\sqrt{4942}}{4}
$