(2x-4)(x+6)=1000

Solution for (2x-4)(x+6)=1000 equation:

(2x-4)(x+6)=1000

We move all terms to the left:

(2x-4)(x+6)-(1000)=0

We multiply parentheses ..

(+2x^2+12x-4x-24)-1000=0

We get rid of parentheses

2x^2+12x-4x-24-1000=0

We add all the numbers together, and all the variables

2x^2+8x-1024=0

a = 2; b = 8; c = -1024;
Δ = b2-4ac
Δ = 82-4·2·(-1024)
Δ = 8256
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:

$\sqrt{\Delta}=\sqrt{8256}=\sqrt{64*129}=\sqrt{64}*\sqrt{129}=8\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{129}}{2*2}=\frac{-8-8\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{129}}{2*2}=\frac{-8+8\sqrt{129}}{4}
$