x=100-0.5x(2x-x)

Solution for x=100-0.5x(2x-x) equation:

x=100-0.5x(2x-x)

We move all terms to the left:

x-(100-0.5x(2x-x))=0

We add all the numbers together, and all the variables

x-(100-0.5x(+x))=0


We calculate terms in parentheses: -(100-0.5x(+x)), so:

100-0.5x(+x)

determiningTheFunctionDomain
-0.5x(+x)+100

We multiply parentheses

-0x^2+100

We add all the numbers together, and all the variables

-1x^2+100

Back to the equation:

-(-1x^2+100)


We get rid of parentheses

1x^2+x-100=0

We add all the numbers together, and all the variables

x^2+x-100=0

a = 1; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·1·(-100)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{401}}{2*1}=\frac{-1-\sqrt{401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*1}=\frac{-1+\sqrt{401}}{2}
$