(x-4)(2x-8)=2800

Solution for (x-4)(2x-8)=2800 equation:

(x-4)(2x-8)=2800

We move all terms to the left:

(x-4)(2x-8)-(2800)=0

We multiply parentheses ..

(+2x^2-8x-8x+32)-2800=0

We get rid of parentheses

2x^2-8x-8x+32-2800=0

We add all the numbers together, and all the variables

2x^2-16x-2768=0

a = 2; b = -16; c = -2768;
Δ = b2-4ac
Δ = -162-4·2·(-2768)
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40\sqrt{14}}{2*2}=\frac{16-40\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40\sqrt{14}}{2*2}=\frac{16+40\sqrt{14}}{4}
$