x=x(16-2x)

Solution for x=x(16-2x) equation:

x=x(16-2x)

We move all terms to the left:

x-(x(16-2x))=0

We add all the numbers together, and all the variables

x-(x(-2x+16))=0


We calculate terms in parentheses: -(x(-2x+16)), so:

x(-2x+16)

We multiply parentheses

-2x^2+16x

Back to the equation:

-(-2x^2+16x)


We get rid of parentheses

2x^2-16x+x=0

We add all the numbers together, and all the variables

2x^2-15x=0

a = 2; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·2·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*2}=\frac{30}{4}
=7+1/2
$