x=10x(9-3X)

Solution for x=10x(9-3X) equation:

x=10x(9-3x)

We move all terms to the left:

x-(10x(9-3x))=0

We add all the numbers together, and all the variables

x-(10x(-3x+9))=0


We calculate terms in parentheses: -(10x(-3x+9)), so:

10x(-3x+9)

We multiply parentheses

-30x^2+90x

Back to the equation:

-(-30x^2+90x)


We get rid of parentheses

30x^2-90x+x=0

We add all the numbers together, and all the variables

30x^2-89x=0

a = 30; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·30·0
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*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*30}=\frac{178}{60}
=2+29/30
$