180-x=3x(90-x)

Solution for 180-x=3x(90-x) equation:

180-x=3x(90-x)

We move all terms to the left:

180-x-(3x(90-x))=0

We add all the numbers together, and all the variables

-x-(3x(-1x+90))+180=0

We add all the numbers together, and all the variables

-1x-(3x(-1x+90))+180=0


We calculate terms in parentheses: -(3x(-1x+90)), so:

3x(-1x+90)

We multiply parentheses

-3x^2+270x

Back to the equation:

-(-3x^2+270x)


We get rid of parentheses

3x^2-270x-1x+180=0

We add all the numbers together, and all the variables

3x^2-271x+180=0

a = 3; b = -271; c = +180;
Δ = b2-4ac
Δ = -2712-4·3·180
Δ = 71281
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{-(-271)-\sqrt{71281}}{2*3}=\frac{271-\sqrt{71281}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-271)+\sqrt{71281}}{2*3}=\frac{271+\sqrt{71281}}{6}
$