(320+8x)(x-2)=320x

Solution for (320+8x)(x-2)=320x equation:

(320+8x)(x-2)=320x

We move all terms to the left:

(320+8x)(x-2)-(320x)=0

We add all the numbers together, and all the variables

(8x+320)(x-2)-320x=0

We add all the numbers together, and all the variables

-320x+(8x+320)(x-2)=0

We multiply parentheses ..

(+8x^2-16x+320x-640)-320x=0

We get rid of parentheses

8x^2-16x+320x-320x-640=0

We add all the numbers together, and all the variables

8x^2-16x-640=0

a = 8; b = -16; c = -640;
Δ = b2-4ac
Δ = -162-4·8·(-640)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-144}{2*8}=\frac{-128}{16}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+144}{2*8}=\frac{160}{16}
=10
$