(x)(320-8x)=(x)

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

(x)(320-8x)=(x)

We move all terms to the left:

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

determiningTheFunctionDomain
x(320-8x)-x=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+x(-8x+320)=0

We multiply parentheses

-8x^2-1x+320x=0

We add all the numbers together, and all the variables

-8x^2+319x=0

a = -8; b = 319; c = 0;
Δ = b2-4ac
Δ = 3192-4·(-8)·0
Δ = 101761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{101761}=319$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(319)-319}{2*-8}=\frac{-638}{-16}
=39+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(319)+319}{2*-8}=\frac{0}{-16}
=0
$