(2x-4)(x+8)=42*24

Solution for (2x-4)(x+8)=42*24 equation:

(2x-4)(x+8)=42*24

We move all terms to the left:

(2x-4)(x+8)-(42*24)=0

We add all the numbers together, and all the variables

(2x-4)(x+8)-1008=0

We multiply parentheses ..

(+2x^2+16x-4x-32)-1008=0

We get rid of parentheses

2x^2+16x-4x-32-1008=0

We add all the numbers together, and all the variables

2x^2+12x-1040=0

a = 2; b = 12; c = -1040;
Δ = b2-4ac
Δ = 122-4·2·(-1040)
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-92}{2*2}=\frac{-104}{4}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+92}{2*2}=\frac{80}{4}
=20
$