x=x(90-5x)

Solution for x=x(90-5x) equation:

x=x(90-5x)

We move all terms to the left:

x-(x(90-5x))=0

We add all the numbers together, and all the variables

x-(x(-5x+90))=0


We calculate terms in parentheses: -(x(-5x+90)), so:

x(-5x+90)

We multiply parentheses

-5x^2+90x

Back to the equation:

-(-5x^2+90x)


We get rid of parentheses

5x^2-90x+x=0

We add all the numbers together, and all the variables

5x^2-89x=0

a = 5; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·5·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*5}=\frac{178}{10}
=17+4/5
$