x=3x(180-x)

Solution for x=3x(180-x) equation:

x=3x(180-x)

We move all terms to the left:

x-(3x(180-x))=0

We add all the numbers together, and all the variables

x-(3x(-1x+180))=0


We calculate terms in parentheses: -(3x(-1x+180)), so:

3x(-1x+180)

We multiply parentheses

-3x^2+540x

Back to the equation:

-(-3x^2+540x)


We get rid of parentheses

3x^2-540x+x=0

We add all the numbers together, and all the variables

3x^2-539x=0

a = 3; b = -539; c = 0;
Δ = b2-4ac
Δ = -5392-4·3·0
Δ = 290521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{290521}=539$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-539)-539}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-539)+539}{2*3}=\frac{1078}{6}
=179+2/3
$